Transgender people have erupted into the news in the past couple of years, whether it’s Caitlyn Jenner’s glamour pose on the cover of Vanity Fair or Eddie Redmayne portraying a trans woman in The Danish Girl. Jack Monroe transitioning made the headlines, and there was also the jolt of a macho boxing promoter emerging like a butterfly as Kellie Maloney.

Each celebrity transition is inevitably a big news story. Partly from prurience, pondering about what other people do with their genitals. But mainly because trans seems transgressive in the most fundamental way. Trans people may just try to live as themselves, not making statements or gestures – but the trans idea threatens the fundamental social laws that we are each assigned a God-given role on Earth at birth by gender: nothing is more revolutionary than questioning that. Feminism was always revolutionary: no wonder the trans issue has split even that movement, though feminism’s failures have often been caused by fissiparous factionalism, with serial “cat-fights” to thrill its many opponents.

Parliament, as ever, takes its time to catch up, but today Maria Miller’s women and equalities committee publishes a sensible and humane report that starts to tackle the real pain and suffering society causes to transgender people, far from Hollywood or magazine covers. With 30 recommendations to improve life for trans people, the report calls for full trans equality within six months. The NHS comes out badly in this report, from ignorant and dismissive GPs through to three-year waits for a first appointment at gender identity clinics. NHS England admitted that trans and non-binary people were a “hidden”, badly treated group. If the NHS apportioned funds according to intensity of suffering, mental health would be a top priority – and so might gender identity treatment. The report calls for 16-year-olds to get official recognition of a new gender and for police to be trained in transphobic hate crime.

The picture that emerges is – unsurprisingly – of bullying, harassment and often lives of torment. Official attitudes imply these are people making frivolous lifestyle choices about their gender and sexuality – exactly the accusation lesbian and gay people always endured and often still do. Gay marriage may be the law, but less has changed under the surface, away from the Graham Norton show: ask Stonewall about the distress calls they get. The reality for many gender-variant people is bullying, beatings-up, and for too many of the young, suicide attempts.

But why quite so much fuss? There are relatively few trans people, and there are many brutally bullied minorities of all kinds. Is it just fascination with the apparently outlandish? No, for both feminists and anti-feminists, trans issues strike at the heart of the matter – what is it to be a woman? In the feminist split, I can see both sides. Germaine Greer, as ever happy to jump on landmines, rebelled at the idea that transgender women are “women”: she says women need a “big … smelly vagina” to qualify. To many, the styling of Caitlyn Jenner in silver glam, semi-nude outfits is an affront. Why does Kellie Maloney choose to be so frilly feminine? To some they are maintaining the worst stereotypes of femininity that feminism is trying to escape. Or at least some feminists: others joyfully embrace high heels and lipstick and why not?

Trans people didn’t choose to become the pivotal point in the mighty “what is a woman question”. Everyone has their own destinies. That should be no one else’s concern. Let men and woman be and dress and think as they choose.

Here’s why feminists should embrace the debate, and embrace trans people, whatever their dress style. The gender spectrum has always run from a few extreme males to a few extreme females, with most people clustered around the middle. Studies trying to assess “male” and “female” psychological characteristics always find a great crossover – but suffer from the problem of deciding in the first place what is defined as a male or female characteristic. None of us can know how much we are conditioned by chemistry, how much by society – but as women gradually get freer, they get more “male”, or what used to be called male. Children are forced from birth into fixed roles too extreme for most and it’s got worse. There is more “princess on board” pinkification, girls mocking other girls who won’t pinkify, with more torment over body shape and appearance than when my daughters were at school. It still takes Bend it Like Beckham boldness to play football for a lot of girls. Boys likewise are forced to be boys. Welcome everything that breaks down gender, a spectrum where anyone is free to be and do what they please, the more genderqueer, the freer. Good news that the committee suggests anyone can put X on their passport, not M or F.

Feminists shouldn’t be side-tracked into “what is a woman?” theology when most women still confront the same basic old barriers: how do you bring up children and have a career? Why are you paid less? Why do you own less? Why are you more powerless? Why are women prone to assault, mockery and contempt? How do you live with a man? How do you bring up sons? How do you be human first?

When we’ve dealt with all that and gender no longer defines us so brutishly, there may be time to debate the finer points; meanwhile, let’s welcome anyone into the sisterhood, which is already furiously diverse.

• This article was amended on 14 January 2016 to more accurately represent Germaine Greer’s comments on transgender women