Should you be struggling with a gift idea for that special person in your life, here’s a suggestion: how about a home DNA kit? These are all the rage in America, I recently read in the New York Times, with 3m sold by ancestry.com alone in the past five years. At last, Americans can find out how Irish they actually are.

On the one hand, this makes sense: identity is the hot issue of our age. On the other, it makes no sense at all, because your identity is, we keep being told, whatever you want it to be. And, indeed, the New York Times writer stoutly concluded, “Whatever the results, I’ll still come from a large Irish family.” Top o’ the morning to you, sir: why let a blood test ruin your St Patrick’s Day?

Nowhere is the discussion about identity more passionately felt than within the transgender movement. If you feel you are a woman, you are a woman is the rule, although some women are querying this. Last week, the novelist Chimamanda Ngozi Adichie was asked by Channel 4’s Cathy Newman whether trans women are “real women”. “My feeling is trans women are trans women,” Adichie replied, a response not so much tautological as almost palindromic. “I don’t think it’s a good thing to conflate everything into one.”

This was a clearer way of saying what Jenni Murray had written in an article that clumsily argued trans women are not “real women”. And as with Murray, the online opprobrium quickly rained down on Adichie’s head. The next day she posted a clarification on Facebook, but stood her ground: “Acknowledging differences and being supportive are not mutually exclusive,” she wrote.

The fear of being on the wrong side of history is a strong persuader, and it was clearly behind much of the reaction to the news that the BBC had slapped down Murray. Instead of crying foul at the broadcaster’s palpably nervy excuse that their presenters must remain “impartial on controversial topics” (while having no problem with Gary Lineker sharing his political views), female commentators gave Murray a kicking. Let all women be women, was the verdict.

This kumbaya approach is an increasingly popular one. Why can’t we ladies all just get along? Hakuna matata! Yet no one is asking why more women than men are raising objections here. Perhaps people think this is just what women are like: uniquely catty. Lifelong feminists, especially older ones, who express any reservations about eliding the experiences of trans and cis women are dismissed as bigoted ol’ bitches – and maybe some are. But there are real ethical issues here, and they overwhelmingly affect women.

Sport is one obvious example. Male-born bodies have had different testosterone levels and muscle distribution from female ones. No one knows what the solution is but pretending there isn’t a difference is ridiculous. Then there are prisons. It’s easy to cheer on Chelsea Manning, but should anyone with a history of crimes against women and girls really be in a female prison?

In January, it was reported that the British Medical Association advised that instead of referring to “expectant mothers”, health providers should talk about the less exclusionary “pregnant people”. Some young feminists are even asking if it’s OK to use the words “female” and “woman” – yet men are not being urged to avoid mentioning their gender. Is it any wonder some women are calling bullshit?

Just as the fringe elements of the political world have taken centre stage, so the more extreme end of the trans movement – which insists there are no differences between trans and cis women – has moved to the frontline. Some will call this progress; to me, it seems more a case of throwing out the commonsensical baby with the transphobic bath water. Trans activists say the idea that biology should determine who is and isn’t a woman is misogynistic. Yet far more simplistic gender arguments are advanced by the trans movement. On Radio 4’s PM last autumn – from the impartial BBC – a mother went unchallenged when she claimed she realised her three-year-old daughter was a trans boy when she asked for books about pirates instead of princesses. In another BBC interview last year, Eddie Izzard said he loves manicures because he’s trans.

That trans people have long suffered from hideous prejudice and violence, and continue to do so, is without question. But as Adichie said, acknowledging differences and being supportive are not mutually exclusive. If anything, they go hand in hand, because they allow women, trans and non-trans, to talk honestly and see each other as people, instead of reducing themselves to manicures and menstruation.

• This article was amended on 12 February 2019 to remove a reference to the imprisoned Ian Huntley after the Daily Star Sunday published on 10 February 2019 a clarification of its earlier reports. The clarification stated in part that “Ian Huntley would like to make it clear that he…has never asked to be addressed by any name other than his own and that there has never been a plan for him to change his gender identity.”