Ayaan Hirsi Ali enters an apartment in New York followed by a bodyguard. The 40-year-old, who for the last six years has been unable to turn up at a venue without it being checked by security, is a writer, polemicist and critic of Islam. She is also a Somali immigrant, an ex-Muslim, a survivor of child genital mutilation, an exile many times over, a former Dutch MP, a black woman whose language would not, in places, look amiss in a BNP pamphlet, a remarked-upon beauty and a lady-in-peril, identities that lend her as a figurehead to disparate causes and bring on confusion in the people she meets.

"I'm a serious person," she says, frowning, as the photographer suggests various fashion poses, but she is also quietly, almost coyly glamorous, moving around with fawn-like grace. It's a combination that works particularly well on male polemicists of the muscular left, who can't do enough to defend her: her gentle charm, her small wrists, her big eyes – oh, and her brave commitment to Enlightenment values – in the face of all that extremism.

It was after fleeing an arranged marriage and settling as an asylum-seeker in Holland that Hirsi Ali converted from Islam to atheism with the kind of zeal that usually powers journeys going the other way. She can, she has said, make statements that a white person simply could not: on the "dangers" posed to the west not just by radical, but by regular Islam; on the "backward" nature of the religion; on how "terrible" the Qur'an is; and, in the most startling argument of her new book, Nomad (a follow-up to her bestselling memoir Infidel), how Muslims would do well to learn from Christianity. She is aware of the liberal twitching she causes – what if accusing her of racism is in itself racist? What if her experience trumps all other arguments? In 2004, after her friend Theo Van Gogh, the Dutch journalist with whom she made a film about women and Islam, was murdered, she was put under 24-hour security. (In the US it is paid for by private donors; when she returns to Europe, where she is still a Dutch citizen, she is protected by the state.) Two years later she left Holland following a controversy around her citizenship and for the last three years she has worked in Washington for the American Enterprise Institute, a rightwing thinktank, contributing papers on how the failures of multiculturalism have allowed for the rise of Islamic extremism in the west.

The accusation that most irritates her – that the events of her life have left her "traumatised" and an easy pawn for rightwing politicians – is, as she says, a sexist presumption. And yet the suspicion remains: that those convictions one arrives at – and fights hardest for – via fraught personal experience are emotional, not rational, and as such beyond reach of most useful debate.

"I'm not being rightwing," she says. "The people who believe themselves to be on the left, and who defend the agents of Islam in the name of tolerance and culture, are being rightwing. Not just rightwing. Extreme rightwing. I don't understand how you can be so upset about the Christian right and just ignore the Islamic right. I'm talking about equality." (She is seeing the rightwing historian Niall Ferguson, who, she wrote recently in a Dutch magazine, she is "enormously in love with", but won't comment on it today, nor smile at the suggestion that in most people's minds this will instantly reposition her on the political scale.)

The impetus to write Nomad came in 2008, when she visited her dying father at a hospital in London and saw her family for the first time in years. The reunion was short and inadequate, and brought about "the horrible feelings that come with death; lots of things that I regret". Primarily that she hadn't spoken to him sooner, but also that in what she saw as his internal fight between western and Islamic principles – he believed in educating his daughter, but forced her into a marriage and disowned her when she ran away – the latter won.

Her critique of Islam as a "moral framework not compatible with the modern westernised way of living" is rooted in a critique of her family, her father's unbending will and particularly her mother, a woman who she says was pulled apart by the contradictions of maintaining her faith in a modern society and an identity crisis from which Hirsi Ali herself suffered. (She speaks six languages – English, Somali, Arabic, Swahili, Amharic and Dutch.) The phrasing she uses is startlingly direct. When she writes that "violence is an integral part" of Islamic social discipline, or says in our interview that "Muhammad's example is terrible, don't follow it", it is deliberately, almost narcissistically provocative, the result, one imagines, of a siege mentality and the defensive self-assurance that goes with it. To Hirsi Ali, the act of speaking out, of saying what no one else will say, seems at this stage to be almost a pathology; to override all other considerations.

The subtitle of Nomad is "A personal journey through the clash of civilisations". I ask if she understands why Muslims going about their business are incredibly hurt by these kinds of statements. "But if you compare the reaction of Christians to what is written about Christianity – Richard Dawkins, who's a supporter, says religion is a form of madness – whereby Christians just shrug their shoulders and don't respond. If you compare the way Muslims take offence at perceived insults that are not insults, but are just a critical way of looking at their religion, then I start to ask myself, why are Muslims so hypersensitive to criticism and why don't they do anything with it except to respond by denying it or playing the victim? And I've come to the conclusion it's because of the gradual indoctrination – from parents, teachers – that everything in the Qur'an is true; Muhammad is infallible, you have to follow his example and defend Islam at all times, at all costs. Instead of going along as most people are doing now and saying, OK, let's refrain from criticising Islam, let's refrain from calling Islamic terrorism Islamic, I think we should do the opposite."

When people throw out accusations of racism, she says, they forget that Islam is not a race but a religion; one chooses to follow it. But after 7/7, the racist on the street who's about to beat up a foreign-looking guy doesn't stop to ask him if he believes in Muhammad.

"There is racism that will fall under freedom of expression and there is racism that incites violence or is violent, and those [violent] people have to meet with the law, just like the radical Muslims do. But to say that we are simply not going to talk about Islam – which inspires in today's world the greatest possible danger to world peace – because a few people here and there get offended, I think is the wrong approach.

"The burden of proof now is on the Muslims; if the theology they subscribe to requires you to perform jihad, I think we should engage them by saying, 'Hey, we want to talk about this with you'; that's not to insult you. It is right there in the Qur'an, it is right there in the Hadith, it's been put into practice and it is being preached. And the people who are preaching it are taking advantage of the full array of freedoms that a liberal democratic society has. And we are not going to shut up and call it something else just because you are saying you are offended. I don't even believe they are offended. You should be more offended for the victims of 7/7, [who died] in the name of religion, than by a cartoon that is drawn of Muhammad."

In the new book, Hirsi Ali proposes an "enlightenment project" in which "critical thinking" be introduced to her former faith through various mediums, one of which, she suggests, is the Christian church. "That's probably going to be the most controversial," she says, smiling. I'll say. Even if it didn't ignore the baggage of 1,000 years of history – the Crusades, anyone? Colonialism? – what is an atheist doing promoting Christianity?

Hirsi Ali laughs. She decided to promote Christianity, she says, because of letters she received after Infidel was published, from Muslims who were sympathetic to her cause but were reluctant to abandon their faith altogether. "Some say, 'Oh, I have also become an atheist and I'm happy to have shed that cruel nonsense off.' But then some say, 'I don't want to become an atheist.' " Hirsi Ali dismisses the kind of Christians who picket abortion clinics as fringe elements within a faith that, generally, "talks about a concept of God that is different from the Muslim [concept], where you are required to submit your will completely and conform to what is in the Qur'an. I talk about a Christianity that is enlightened enough to separate spirituality from the rest of life. Not just church and state, but knowledge and church. Religious groups not telling you what you can and can't do, but religion becoming an inside thing. It's very hard for me to describe a thing that I don't have – that kind of spirituality."

The 11-minute film Hirsi Ali made with Theo Van Gogh, broadcaster and provocateur who publicly referred to Muslims as "goat-fuckers", was intended to symbolise what they saw as misogyny within Islam. In it, a half-naked woman is depicted with lash marks on her back while a voiceover reads passages from the Qur'an; elsewhere, Qur'anic excerpts relating to the submission of women are projected on to a woman's naked back. As Ian Buruma reported in his excellent book Murder In Amsterdam, when a Dutch news programme aired Submission to Muslim women in a shelter for victims of domestic violence, they were by and large appalled. These were the very people Hirsi Ali was trying to help; but her style, and her choice of cohort, offended them. Three months after the film aired on Dutch TV, Van Gogh was murdered in the street by Mohammed Bouyeri, a Dutch-Moroccan who pinned a note to his chest, calling for holy war and naming Hirsi Ali as a target.

At the time, she was an MP in the Dutch parliament, an extraordinary ascent given that 12 years earlier she had entered the country with barely a suitcase. In 1992, Hirsi Ali was en route from Kenya to Canada to begin married life with a man for whom she had no respect. During a stopover in Germany, she gathered her courage and, on the advice of a relative with knowledge of the asylum system, took a train to Holland. (Her first choice was Britain, but she was told crossing the Channel would be too difficult.) Holland, she was assured, had one of the most liberal asylum policies in Europe. So began a decade during which she rose from a minimum wage job, to a degree in political science from the University of Leiden and up through the Dutch political establishment.

The uncompromising tone of Submission was inspired, in part, by Hirsi Ali's experiences in those early years as an interpreter for social services, hearing stories that took her back to her childhood. Her father was a political opponent of the Somali president Siad Barre. When she was two, he was jailed, forcing the family to flee, first to Saudi Arabia, then Ethiopia, then Kenya. Although there is in Hirsi Ali an almost aristocratic bearing, it was not an easy upbringing; she was beaten by a religious teacher until a rib broke; was, at her grandmother's insistence and in her father's absence, subjected to genital mutilation; and in later years would watch as her sister crumbled into mental illness after a secret abortion – all acts that she believed to be sanctioned by her faith and which, as she started work in Holland, she believed the Dutch authorities wilfully ignored. When Muslim women in the Hague were found to have high instances of vitamin D deficiency, health workers put it down to poverty and not, as Hirsi Ali says came out in the interviews, to the fact they were deprived of sunlight because they didn't have permission to leave the house until their husbands came home at night. She calls this "the twist and turn to avoid Islam". When she had a platform to speak, she resolved, she would not pussyfoot around in the same manner.

And she didn't. After gaining a masters degree, writing a series of pieces in the Dutch press and eventually standing for parliament, Hirsi Ali allied herself with the most unlikely and controversial figures in Dutch politics. As well as Van Gogh, she spoke admiringly of Pim Fortuyn, the Dutch anti-immigration politician who was himself murdered by an animal rights activist. At the end of Nomad, she paints a cosy picture of hanging out in New York with Oriana Fallaci, the late Italian journalist whose post-9/11 polemic, The Rage And The Pride, invokes a seething Muslim mass trying to get into Europe and is described even by Christopher Hitchens, a supporter of Hirsi Ali's, as "a primer in how not to write about Islam". Hirsi Ali says she met Fallaci socially and they didn't talk about Islam – they talked about babies. But to refer to Fallaci so warmly, given her reputation, is of course loaded.

"First of all," she says, "I don't feel that there is guilt by association. And I don't think that human beings are perfect. If Oriana Fallaci wrote – and I have to confess she gave me her books in Italian and I don't read Italian – but if she made these remarks that Christopher says cross the line, it still doesn't mean that she was wrong in her analysis of Islam. OK, she did make mistakes, but she is more of an ally than an enemy." She continues: "If I say, OK, from now I am only going to associate with people who I agree with 100%, that's a very small group of people."

She reserves her greatest disapproval not for writers such as Fallaci, but for intellectuals who she says have failed utterly in their responsibility towards non-white women. The decadence of western feminism is where Hirsi Ali is perhaps strongest. In the book, she attacks Germaine Greer for arguing that female genital mutilation needs to be considered "in context", as part of a "cultural identity" that western women don't understand. Greer, from the quotes Hirsi Ali cites, seems to be arguing merely that female circumcision is at the extreme end of a scale that starts with women wearing high heels for men's delectation – not condoning the former, but condemning the latter as part of a continuum. Hirsi Ali finds this inadequate; a strange, tangential take on the subject. Why, she asks, are voices such as Greer's not speaking out against the subjugation of women in the Muslim world? She calls for a new feminism, "that is going to focus on issues faced by non-western women, because they are the biggest issues. To own your own sexuality, as an adult woman; to choose your own lifestyle; to have access to education [when] what we see in the Muslim world is girls being pulled out of school and married off before they've completed their education. These things, I think, are more basic than the stuff that current feminists are concerning themselves with – like shattering the glass ceiling or finding a balance between work and home life. There was a long article in the New York Times that went on and on about who [in a couple] would load and unload the dishwasher. If you have a career and you're so intelligent, you can work that out. You don't have to have a manifesto. There is feminism that has evolved to a kind of luxury."

On that trip back to London to see her father for the last time, Hirsi Ali visited a cousin on a council estate in east London and saw, with horror, the life she might have led: "on welfare," she says, with hauteur, a virtual "prisoner", in need of her husband's permission to leave the house and then only if encased in a "black shroud". She says: "And I realised, oh my goodness, if I had done what my father wanted me to do in 1992, I would be leading a comparable life, but instead of Tower Hamlets, in Toronto." It is not a portrait she says her cousin would recognise. As far as the cousin is aware, she has made the right choices. How then does Hirsi Ali resolve the Enlightenment paradox of advocating freedom, then turning to other people and saying, I know what's best for you? "But it's not I know what is best for you. Classic liberalism was about the individual; [I am talking about] a denial of rights to an individual within a community: a girl's genitals were being cut; a girl was being denied education, forced into marriage; a gay guy has to hide from his parents that he's gay otherwise they're going to do something to him. That is what liberalism was all about. It is offensive to me if a group of people deny rights to an individual human being in the name of their religion – and they want the rest of us to leave them alone? No way."

Has she been radicalised by her experiences? How can she live with death threats and not, at some level, lose perspective? If she did not have a point, Hirsi Ali says, "there would be no angry Muslims plotting to kill me… people would just be shrugging their shoulders." In any case, she says, living in Washington with security is still better than living as a woman in Saudi Arabia without it. "Even with protection, even with death threats, I can publish, I can travel and I can live the life that I want, and not the one my parents want, or some imam somewhere thinks I should live."

She is not interested in going back into politics and believes she has more influence on the outside. She is sceptical of Obama, who, she thinks, in his speech to the Muslim world in Egypt last year was optimistic to the point of delusion. She says: "The idea that if people are just friendly and demonstrate they want peace, that will be answered with good will – that is really naive. If you have organisations in the US that are lobbying him and Congress to allow sharia, then being nice to them is not enough." In terms of British politics, she is more impressed with Labour than the Conservatives, for their suggested ban on the group Islam4UK. The Archbishop of Canterbury may be surprised to know she considers him an "appeaser" of Islam for considering limited introduction of sharia law.

The book ends with a letter to her unborn, and as yet unconceived, daughter. Hirsi Ali draws a line from her grandmother, a nomad who followed the tribal religious code, to her mother, caught between tribalism and modernity, to what she hopes would be her daughter's uncomplicated relationship with the west. "She would," she says, "not have to deal with the identity crisis that I and my mother had to deal with."

Hirsi Ali misses Dutch bread and cheese; but when she lands at JFK, these days, she thinks, "home". And Africa? She smiles. "I don't have much in me left for Somalia, because the country is so broken, it's not realistic to daydream about it." There is one thing, she says, that annoys her about the way her former faith is depicted. "There is this tendency to think that if you are a Muslim woman you are not strong." She repositions. "They," she says firmly, "are strong women."

• Nomad: A Personal Journey Through The Clash Of Civilisations, by Ayaan Hirsi Ali, is published by Simon & Schuster at £12.99. To order a copy for £9.99 (including UK mainland p&p), go to theguardian.com/bookshop.