IT seems no-one saw Donald Trump’s latest headline-grabbing edict coming. Even those who lobbied him to restrict healthcare provision for US service personnel have been wrong-footed by his assertion that his government “will not accept or allow transgender individuals to serve in any capacity in the US military”.

What exactly do the president’s tweets mean? His reference to “tremendous medical costs” strongly implies he is referring to sex reassignment surgery – the costs of which have provided the spurious basis for Republican politicians to make trouble here. But the category “transgender” covers a hugely diverse range of people, not just those who seek to have their genitals surgically altered. A 2016 research review estimated there were about 2500 transgender active service personnel in the US, and that between 29 and 129 could be expected to “seek transition-related care that could disrupt their ability to deploy” every year. To put these figures in perspective, that’s 29 to 129 out of 1.3 million.

As a money-saving measure, the blanket ban makes no sense at all. As commentators have been quick to point out, the cost of transitions – estimated at between $2.4million and $8.4m per year – is a drop in the ocean compared to the $40m the military spends on Viagra, and in any case the focus on these costs assumes all trans-identifying people seek some kind of medical assistance with transition. They don’t.

So who was lobbying for a solution to this non-problem, and why? If you were playing a game of bigot bingo you’d be lucky to draw a card based on Vicky Hartzler, whom the people of Missouri elected to the House of Representatives in 2010. Anti-immigrant? Check. Anti-abortion? Yes ma’am. Climate change denier? You betcha. She has questioned the authenticity of Barack Obama’s birth certificate, backed cuts to the food stamps budget, and written a book titled Running God’s Way: Step by Step to a Successful Political Campaign. She opposes same-sex marriage and was once described by US magazine Mother Jones as the “most anti-gay candidate in America”.

No-one with a heart and a brain would want to be on Team Hartzler. Certainly no-one who identifies as progressive, liberal or feminist. She’s a bogeywoman, a parody of a Christian fundamentalist politician, a punchline made flesh. Her stance on transgender soldiers is clearly part of a broader anti-LGBT agenda that has nothing to do with her country being “combat-ready” and everything to do with personal distaste.

But in a topsy-turvy way, people like Hartzler may prove to be a gift to the trans activism cause.

Last week on these shores, you couldn’t switch on the news or open a paper without hearing about gender. The BBC’s salary list sparked countless conversations about closing the “gender pay gap”, and politicians from the left and right lined up to back review of the Gender Recognition Act, which sets out bureaucratic and medical barriers that must be overcome before a transition can be legally recognised. The problem with discussions of both is that we aren’t actually talking about gender at all – we’re talking about sex.

Gender is not a biological reality, but a restrictive social construct, and there’s no good reason for the government to take any interest whatsoever in whether a citizen conforms to a gender role. And when we talk about the gender pay gap we are speaking euphemistically. What we mean is the sex pay gap – the difference in pay for men and women.

Gender roles matter to people like Vicky Hartzler, who has voted down legislation to address violence against women and whose efforts to restrict gay rights are thwarted by the idea that a woman can become a man and a man can become a woman. But they also matter to many trans activists, whose motives – when scrutinised – are every bit as homophobic.

“Are genital preferences transphobic?” asks vlogger Riley Dennis in a recent video for the Everyday Feminism website. Riley, who identifies as a nonbinary lesbian, says the answer is complicated. After all, aren’t many sexual preferences informed by society? Doesn’t it therefore follow that lesbians who decline to have sex involving penises are transphobes?

Clearly no, it does not. Same-sex attraction is just that – attraction to people of the same sex. Homosexuality is not a lifestyle choice, or a prejudice, or a deluded response to binge-watching episodes of Ellen. But Dennis dismisses charges of homophobia with a linguistic sleight of hand: lesbians are “women who only like women”, and transwomen are women.

This gradual erasure of women as a sex category, as opposed to a “gender”, has not gone unnoticed. Lesbian women and their heterosexual allies see all too clearly how the needs and desires of people with penises are starting to be centred in debates about women’s rights. Many transwomen see it too, and are both dismayed and fearful about the consequences. These women are ready to make their voices heard, and to express concern that so-called “gender equality” cannot be addressed until we stop blushing and start using the word “sex”.

If, after all the evidence is examined, self-declaration of sex is rejected in the UK, the likes of Vicky Hartzler will doubtless cheer from across the pond. But this should be seen as nothing more than an irrelevant distraction. American right-wingers might not care about transgender people, but they sure as hell don’t care about women either.