Let’s not beat about the bush, although that’s not the happiest phrase in the light of what I’m about to say. Germaine Greer’s views on transgender people are based on the kind of quasi-Freudian cod-psychology you’d think a feminist critic would find embarrassing. In 1999’s The Whole Woman, she wrote that “when a man decides to spend his life impersonating his mother (like Norman Bates in Psycho), it is as if he murders her and gets away with it”. Today, her views have the same thrust – that it’s not possible to change from a man to a woman – although their expression is usually less aggressive. She told Newsnight on 23 October, for example, that she will use whatever pronouns people ask for, and would not try to limit sex reassignment surgery for those who want it.

Still, this is normally the point where I start humming “Bridge Over Troubled Water”. In the age where Caitlyn Jenner is set to be crowned Glamour’s Woman of the Year, after living as one for less than 12 months, Greer is wildly out of step with public opinion. But then, when was she ever not? She is a controversialist, a provocateur – she has never wanted to be an unsung foot soldier of the feminist movement; she always wanted to be its Camille Desmoulins. I’ve just finished reading Gloria Steinem’s memoir, and it’s full of warm references to other feminists. A Greer autobiography would be unlikely to strike the same sisterly tone.

I mention her controversial opinions on transgender issues because they are what prompted Cardiff University Women’s Society to try to have Greer disinvited from speaking. (She has now pulled out anyway, saying she is “too old” at 76 to face protesters*.) She joins a small but growing list of feminists deemed unacceptable to address students: the NUS has an official policy of no-platform against Julie Bindel because she “is vile”. Neither of these women has advocated or incited violence, which used to be the old rationale for “no platform”. Their words are the problem.

It’s interesting that it is Greer's views on gender that are the flashpoint, because she has been flat wrong about many things in her career – FGM, for example, which she has defended given its “cultural” element – without anything like the same backlash. Put simply, trans issues are the new dividing line for progressive activism; the way for younger activists to kick against their foremothers in the feminist movement. Feminists are like Batman: they either die heroines, or live long enough to become villains.

With gay marriage now legal in America, there is also the sense among online social justice communities that trans rights are “the new civil rights frontier” (as Time magazine wrote next to a photo of the Orange Is the New Black star Laverne Cox). Social media has acted like an accelerant on this fire: sites like BuzzFeed and Huffington Post’s LGBT section offer uplifting tales of transgender children’s achievements and famous adults coming out, alternating with occasional three-minute hates for “TERFs” (trans exclusionary radical feminists), a group who are said to be inciting violence against trans women by refusing to accept them as women. Sharing such articles has become a badge of progressive correctness. The word “TERF” is sprayed around like confetti, with very little understanding of what it means. I’ve been called a TERF, even though I think trans women are women and absolutely have a place in feminism. I think it’s become a politer way of saying “witch”.

It’s also about undergraduates rebelling against their parents’ generation and its liberal deification of free speech. After all, the last time students tried to have Greer disinvited from addressing a university crowd, one of those defending her right to speak was Rachael Padman, the trans academic whose appointment to the all-women’s college Newnham Greer tried to kibosh in 1996. Padman said she hoped the Cambridge Union would “give Germaine a fair hearing, but of course robustly interrogate her”. Here was someone directly affected by Greer’s beliefs, defending her right to express them.

The fact that the trans rights struggle is the first progressive cause to come of age in the time of Twitter leaves anyone who wants to explore the thorny issue of gender and biological sex, and the meaning of both and the differences between them, in a difficult position. I accept completely that transgender people face difficulties in their life that I, with a far less uneasy relationship with my body, struggle to comprehend. Last week I invited an educational organisation called All About Trans in to talk to the editorial team. Some of the stories were difficult to hear: family rejection, suicide attempts, street harassment.

But several guests also said things which have become unsayable on social media, even by trans people themselves: one referred to using the term “trans*” (the asterisk denotes that the term includes not just transgender people, but those who reject the gender binary, or are otherwise genderfluid) and was told, laughingly, by others that this was very two years ago. There are places on the internet where you will be told to “die in a fire” if you write “transwomen” instead of “trans women”. (Not pressing the spacebar is said to indicate that you don’t believe they are real women).

After a while, you begin to wonder if the opacity of language isn’t accidental at all. Trans activists, tired of being treated as objects of curiousity, fear or pity by outsiders, have decided to seize control of the discourse and develop their own ways of talking about how they feel. This is understandable, but it also means that everyone is constantly making mistakes. This would be OK – in everyday life, people slip up and get corrected, and the world keeps turning – but because it's happening in the crucible of social media, where women's opinions carry a higher cost, censure for those mistakes is distributed unfairly. There are phrases that a man could say – "female socialisation" springs to mind – with no comeback, but would be read as Deep TERF Code coming from a feminist's mouth. I've lost count of the number of times that male friends have expressed surprise that their normally quiet, polite Twitter experience suddenly turns into a hornet's nest if they chat with me about a controversial divide in feminism.

Even trans people who do not have the “correct” opinions feel worried about broaching the subject; I know a group of “gender critical” trans women who are castigated regularly as “TERF tokens” and “Uncle Toms”. (Putting paid to the flatulent piety so often circulated on social media: “Why don’t you just listen to trans people?” Because it turns out, O Wise One, that minority groups are not homogenous.) Like so much of modern activism, the urge here is to conflate identity and opinion. It's a useful, forceful rhetoric tactic – it personalises the fight – but it also allows all kinds of sleight-of-hand. If you "listened to women" on abortion, you'd hear a much higher level of anti-abortion views than if you listened to men, for example. What people mean when they say that is "listen to mainstream feminist opinion". But that doesn't have quite the same snappy righteousness, though, does it?

Although trans issues have benefited hugely from the speed and reach of online activism, in other ways they have been ill-served by being the first progressive cause to blossom fully in the social media age. Nuance is impossible. Dare to write anything other than a saccharine celebration of diversity, or solemn sermons about how brave trans people are, and your opinion is read as an attack on the very idea that they should be allowed to carry on living at all. But rainbow avatars and “inspirational” stories will only get you so far. There are hard questions that we need to address as trans people become more visible and we try to take their needs into account in public policy. Should we abolish single-sex schools, for example, when they make life so much harder for teenagers who decide that they wish to live as the opposite gender? Should trans women who have gone through puberty as boys be allowed to compete in women’s sports and are cis women who do not want to compete against them bigots? Should a person with a penis and beard (no surgery or hormones are required to legally transition) be allowed into a women-only rape shelter? Should gender non-conforming children have access to "puberty blockers" at 16? At 12? At eight?

In my Pollyanna-ish way, I hope that all of these questions can be resolved with respectful negotiation; but there will have to be compromises between competing interests. It’s not – as many people on Twitter seem to believe – as simple as identifying the group you feel is most fashionably oppressed and sprinting to shout: “Solidarity!” And God save us from all the progressive men who will never face the sharp end of such questions – who have never had to think about rape shelter policy, for example – using this issue to show how right-on they are. Come on, feminists, they chirrup without self-awareness. Stop being so uptight!

You can see this in the way the word "TERF" has moved way beyond its initial, perhaps useful meaning – to describe a political position – to encompass any woman who disagrees with or even questions others who have strongly held views on gender. It is, sadly, a thought-stopping cliché. Being a TERF is bad. I don’t want to be called a TERF. I should not speak to TERFs in case people think I am one, too.

But here is a list of things which can get you called a TERF, if you are a woman with a public profile: a) believing that biological sex is different from gender, ie that the penis is a male sex organ, even when attached to someone who identifies as a woman; b) believing that being raised as a boy gives you a different experience of life from anyone raised as a girl; c) believing that you need to transition using surgery or hormones to be trans (a recent BuzzFeed piece was headlined “This Trans Women Kept Her Beard And Couldn’t Be Happier”); d) believing that someone who transitions at 45 has not “always been female”.

I’d argue that those positions are far removed from the hateful, discriminatory behaviour and speech which most of us would accept is transphobic. And it is entirely possible that some or all of them will seem completely outdated in 50 years as our ideas about sex and gender move on. But they don't seem to me to be in themselves vile or beyond the pale.

Yet there is now a strange conflation of rhetorical with actual, physical violence. Such views are said to lead directly to the dehumanisation of trans people that puts them in danger of street attacks and death. It is a difficult point to argue when confronted with the facts: the only person convicted of murdering a trans woman in Britain this year is Joaquin Gomez-Hernandez, who killed his wife, Vanessa Santillan, after finding her in bed with a client. He had no job, and lived off her earnings as a sex worker; a familiar tale of a bruised male ego curdling into rage. Not an avid reader of Germaine Greer, I would guess.

This is a subject I have been reluctant to write about, for several reasons. The first is the abuse and shouts of “TERF” that will follow; despite having views on the issue which I’d guess are more progressive than 95 per cent of the population, there might be attempts to no-platform me in future. The second is a desire not to alienate trans activists, many of whom I personally know and respect, or to make their lives harder.

From the trans perspective, I can understand the feelings that the gains the movement has recently made are both recent and fragile, and the desire to set the terms of the debate after so long being treated as objects of pity or ridicule. After all, the challenges of transition are a daily task for many people, not a theoretical debate. But the subject has become part of a society-wide conversation; to move on, it must be something that ordinary people, outside the charmed circle who know that trans no longer takes an asterisk, can have an opinion on.

The current orthodoxy is that issues should be left to those directly affected by them to discuss, but consider this for more than a minute and the absurdity reveals itself. The rights of severely disabled people who cannot communicate would, under this logic, never get discussed. Plus: gender affects us all; free speech affects us all. Men have the luxury of not needing to have an opinion on whether it is a good idea for women’s sports to be opened to trans women, or for women’s refuges to be accessible to those with penises; feminists do not. Plus: I'm a journalist. My job is to write about other people. The rise of the First Person Industrial Complex is not an unalloyed good.

Can we all be honest here? No one has a bloody clue how much of gender is innate, and how much is socially constructed. Scientific research shows some differences between male and female brains in aggregate, but if shown a random brain, it is impossible to say it definitely belongs to someone with XX or XY chromosomes. In any case, brains are incredibly plastic, responding to their environment. Perhaps studies of identical twins could clear this up, but they haven’t done yet for sexuality, so don’t pin too much hope on them. Let’s treat everyone with dignity and respect, while preserving the space to explore this subject scientifically.

Can we also be honest about something else? This battle against Germaine Greer is driven, at least in part, by sexism. After all, the world is full of academics with bad opinions, happily going about their business. Richard Dawkins, for example, is obsessed with proving that a teenage Muslim American boy suspended for bringing a clock to school should not be an object of pity and is instead a cunning hoaxer. David Starkey went on an extraordinary rant on Newsnight a few years ago about how "whites have become black" (ie, were getting involved in street violence). No one is trying to ban him from talking to British universities.

The same students who tried to stop Julie Bindel from talking about free speech (the irony) at Manchester University this autumn did not simultaneously attack her fellow speaker Milo Yiannopoulos, even though his views on transgender people are more extreme than hers. (He believes they are mentally ill and should be denied surgery.) Brendan O’Neill writes almost weekly on the Spectator website that transgender politics is “hocus-pocus”. Where’s the NUS motion condemning him?

On the day the Greer row kicked off, I received a press release from the Cambridge Union saying that students had voted overwhelmingly to offer a platform to Julian Assange, who is an interesting speaker on the subject of internet surveillance . . . and a rape suspect, hiding from a European Arrest Warrant in the Ecuadorean embassy. Because he is a man, he gets to be both.

It is ironic that this debate has focused around the idea of accepting trans women as women, because it also seems to me that we have a problem accepting non-trans women as fully human – a mixture of good and bad, wrong and right. Because, of course, Germaine Greer wasn’t even booked to talk about trans issues at Cardiff: the title of her lecture was “Women and Power: the Lessons of the 20th Century”. As with other feminists, it is assumed that her bad opinions on one subject render her persona non grata on everything else.

Look at the history of no-platforming: it started with organisations like the National Front and the BNP, who trailed thugs and incited violence; then it spread to being used against figures like David Irving, the Holocaust denier – crucially, when he was talking about Holocaust denial. The new no-platforming of feminists means that one duff opinion sees you bundled off the stage, whatever you planned to talk about. Germaine Greer could go to a university to talk about her LP collection and there would be students desperate to ban her.

So yes, trans women are women. They are as much “real women” as I am, given it’s an arbitrary, ever-changing, socially constructed category. But trying to silence those who disagree with that simple statement will dent all women's right to speak. Let she who is without unpopular views cast the first e-petition.

* Update: 2pm, 27 October: Cardiff University have been in touch to say they have subsequently spoken to Greer's representatives, and the event is still scheduled to go ahead next month.