There's a popular student story about Martha Nussbaum giving a talk in a small living room of the Episcopal Church's chaplaincy centre on the leafy campus of the University of Chicago. As she was holding forth, a bird flew down the chimney and started to flutter around the room, bashing into the walls and generally panicking, as trapped birds do. The students were immediately busy opening windows and trying to shoo the poor creature to freedom. All their attention was taken up with the bird. But in the midst of all the excitement, Nussbaum didn't break her intellectual stride. She just carried on delivering the lecture as if nothing whatsoever was going on. She emanates detached academic cool – fully in command of herself and her material. From someone who has spent a distinguished academic career emphasising the riskiness and vulnerability of the human condition, all this slightly frosty control comes as something of a surprise.

Why, she once asked in a brilliant essay entitled "Love's Knowledge", do the gods of the ancient world often fall in love with human beings? Why would they prefer mortals to immortals? It is precisely because human beings are able to fail, she argues, that they are able to manifest so many attractive qualities. Take courage. What place can courage have in the world of immortal gods? How could an immortal god risk everything for another if their own welfare were always guaranteed in advance? And what sort of parent would an immortal parent be to an immortal child? Certainly not one that is up half the night worrying. Risk and vulnerability are intrinsic to being human. And that is what makes us attractive, sometimes heroic.

But up in her office on the fifth floor of the law building, beautifully designed by the Finnish architect Eero Saarinen in the rational style of high modernism, the Ernst Freund distinguished service professor of law and ethics at the University of Chicago does not seem all that much like a risk-taker. She may not be a lawyer, but she chooses her words and her subjects with lawyer-like care. I decide to ask her first about risk and financial markets. It seems a fair enough question, given her interest in risk and the topicality of the issue – and she is famous for having worked with economists such as Amartya Sen and others. But she will not be drawn. "I don't want to talk about the regulation of financial markets because that is not my sphere of expertise. It's a very complicated topic, and if I have written a number of books they are always on topics that I think I know something about."

Her latest book, The New Religious Intolerance, is a vigorous defence of the religious freedom of minorities in the face of post-9/11 Islamophobia. And by minorities she mostly means Muslims. "We see unreasoning fear driving a certain amount of public policy, perhaps more in Europe than in the US," she explains. And Europe has historical form on all this. "The laws that made it illegal to speak Latin in a church but left it legal to speak Latin in universities were covert forms of persecution – and not very covert at all. And you get that all over Europe. You get that in the Swiss minaret case, where a building that expresses the wish of a religious minority is suddenly illegal; you get it in Germany in those cases where nuns can teach in full habit but a teacher can't wear a headscarf."

The reason why the US is better-placed than Europe to deal with its own tendency towards religious intolerance is that "the US has always understood itself to be united around political principles and not around culture, whereas the nations of Europe have a much more traditional conception of nationhood that is connected to romanticism, which thinks of religion and culture as ingredients of nationhood."

There are, she suggests in the book, three basic principles to hold on to: equal respect for conscience, the importance of self-critical vigilance, and the importance of a sympathetic imagination. The first of these, powerfully understood in the US constitution, enshrines legal protection of views that differ from those of the established majority. The state is obliged to adopt a position of neutrality with respect to matters of individual conscience. All human beings are to be afforded equal dignity – a dignity that extends to the ways in which individuals come to understand life's ultimate purpose. Conscience and human dignity are inextricably conjoined.

The role of practical philosophy, as Nussbaum understands it, is to bring these basic principles to bear, and thus to flush out the inconsistency that is a characteristic marker of hidden prejudice. The city of Hialeah, Florida may have passed a law making it illegal to kill an animal in a "public or private ritual or ceremony not for the primary purpose of food consumption" ostensibly on the grounds that it was cruel to animals. But the Supreme Court invalidated this law in 1993, arguing that the same sort of killing, often worse, is permitted in using animals for food. Thus cruelty to animals could not be the real reason for the law: instead, it was clearly drafted in such a way as to target religious practices, something about which the state is obliged to be neutral.

Nussbaum adopts the same sort of strategy when it comes to the burqa. Those who associate the burqa with violence against women are often inconsistent, for instance, in not also wanting to ban alcohol, which is strongly associated with violence against women. Even during prohibition, she points out, alcohol was allowed for religious purposes, such as the eucharist. Many argue that the burqa is something forced on women and that the issue is one of choice. Certainly, if physical coercion is involved or threatened, the law must step in. But what of non-physical forms of cultural or community pressure? Yes, says Nussbaum – such as forcing your child to play the piano or dress smartly or to go into accountancy. The strategy of the book is to reveal the inconsistencies and double standards that we apply to minority religious positions and from there to plead for a more sympathetic hearing of those whose worldviews we do not share.

Her personal motivation for this book is hinted at in the preface, where she describes her conversion to Judaism in 1969, following her marriage to Alan Nussbaum, and her 2008 batmitzvah in the KAM Isaiah Israel congregation, in the wealthy Chicago suburb of Hyde Park, just around the corner from the grand mansions of Barack Obama and Louis Farrakhan. Nussbaum's father refused to come to the wedding. He was, she readily admits, a southern wasp racist, who could not countenance her marrying a Jew. And it is her experience of antisemitism that is at the emotional core of her argument.

"I use the example of antisemitism because I think it is useful to look back to a historical example with some detachment, and we can all admit that mistakes were made. And we can see that the treatment of the Jews was inspired by a kind of concocted fear – so The Protocols of the Elders of Zion is my example – and it has many ingredients in common with fear of Muslims today. What is similar is the demand for a kind of assimilation that extends to dress and ways of life as the condition for full civic equality."

Growing up in a wasp family, "I knew antisemitism very well from the inside". Her father, who came from Georgia, "was a southern racist, and these were very deeply ingrained attitudes. He wouldn't eat a meal with an African American – that sense of physical shrinking, contamination was all over the south."

The more she talks, the more I begin to think that a great deal of her work is a wrestling with the Christian religion of her father – not least with Christianity's nervousness about the body in general and sexuality in particular. A more this-worldly religion such as Judaism is perfectly suited to a philosopher who made her name in The Fragility of Goodness by defending the practical ethics of Aristotle over the metaphysical supernaturalism of Plato. There she argued that Plato, in locating the ultimate source of value outside the human realm, was running away from the inherent riskiness of being human by seeking some extra-human anchor for the permanence of the good life. It's a denial of the intrinsic fragility of goodness, a denial of risk. She agrees with this assessment. "Putting the problems of justice into another world" is the problem she has with Christianity. More recently, however, she has come to a more positive assessment of it. She is full of praise for the Episcopal Church, for the gay bishop Gene Robinson, and its former presiding bishop, Frank Griswold, whom she knew as a teenager in Bryn Mawr, Pennsylvania. "Our Episcopal Church has come a very long way as a force for social progress." But it was while working with the poor in India that she came to see the way in which the Christian teaching that all are made in the image and likeness of God can become a powerful political force for good.

I remind her of an intriguing footnote in "Love's Knowledge" in which she wonders whether Christianity is right that to describe a God who is perfect is also to describe a God that is subject to risk and mortality. Isn't the Incarnation the supreme expression of God's needing to be mortal in order to manifest a fuller ranger of virtues? "It's always been intriguing to me," she admits, "the loveability of mortality." "I just saw Wagner's Ring at the Metropolitan Opera in New York, and that's a huge theme there too. Brünnhilde is playful and powerful, but she isn't really lovable in a deep sense until she becomes human and assumes that vulnerability."