Except that according to polls the public don't want to make it easier to get a GRA, they don't support males in women's sports, and their support for males in women's changing rooms and toilets is dependent on whether they have had genital reconstruction surgery.
It's true that most people don't support the radical TRA agenda, but that doesn't mean that it won't succeed.
This article explains it well:
medium.com/incerto/the-most-intolerant-wins-the-dictatorship-of-the-small-minority-3f1f83ce4e15
It suffices for an intransigent minority –a certain type of intransigent minorities – to reach a minutely small level, say three or four percent of the total population, for the entire population to have to submit to their preferences. Further, an optical illusion comes with the dominance of the minority: a naive observer would be under the impression that the choices and preferences are those of the majority.
TRAs are succeeding in large part by being intransigent, and by making it very, very costly to oppose them.
Notice that they NEVER concede that sexual biology might be relevant to anything, ever: they never say, OK, well we want men to be considered women if they say so, but we understand that sports might be a separate issue; or, we want male prisoners to be housed in women's jails if they desire, but we understand that some dangerous men might exploit this, so for safety reasons not all gender identities should be automatically recognised...
Instead, they unswervingly insist that gender identity trumps biology in all contexts, and then smear and persecute anyone who has the temerity to say, 'Hang on a minute...'. They work to destroy people's reputations and get them fired. They accuse them, baselessly, of causing harm and suicide, making the tenor of the debate so ugly that anyone who values his or her peace and sanity decides it's wiser to just mouth a platitude or not say anything at all. And they don't stop, ever. They are ruthless and relentless. Witness their 5-year-plus smear campaign against US journalist Jesse Singal, because he wrote about the ethical issues around giving puberty blockers and cross-sex hormones to children. The TRAs and their libfem goons spread false rumours that Singal was a sexual harrasser of trans people, lies which they continue to amplify today.
They have not managed to destroy Singal's career, but they have injured his reputation in progressive circles and almost certainly made it impossible for him to be published in mainstream leftist outlets. What is the point of such a campaign, against a journalist who is largely supportive of the TRA agenda? It is to damage and demoralise the individual targeted by it, obviously, but it also serves the larger purpose of demonstrating to other leftist journalists what happens if you scrutinise the paediatric transition industry. What bright, young leftist journalist (or even old and grizzled, for that matter) would dare take on the issue of 'trans' kids in the US today?
Again, witness the campaign against Rosie Duffield, for the crime of stating that women's health messages should reference women. Note that the ferocity of the TRA reaction was totally out of proportion to Duffield's actual comments: she said something very mild that the vast majority of the public would agree with, but the TRAs responded as if her views would horrify all decent and right-thinking people and demanded her expulsion from the Labour Party. This is key to their success: to treat even the mildest dissent from their agenda as the gravest of sins, which somehow erases the humanity of a vulnerable minority and literally causes their deaths. Most people don't have the desire or ability to endure such sustained opprobrium, so most people decide to stay well out of it. This is how 'the most intolerant wins', and how a minority of extremists end up imposing their wishes on the majority.