I am not convinced the UK and Australia are that different.
In the UK, Labour, the Lib Dems, the Greens, the SNP and Plaid Cymru are all uncritical, unquestioning believers in gender identity theory. Only the Conservatives are questioning that narrative. But the Conservatives have been in power for 14 years and on their watch Stonewall has been allowed to run wild, women's single sex spaces and services have become mixed sex and gender confused children have been medicalised. Theresa May wanted to bring in self ID. The conversion therapy ban included trans people until it didn't. There has been a swathe of court cases involving people with gender critical beliefs. None of this would have been allowed to happen if the political environment hadn't been highly favourable towards this movement, and yet the position of all other political parties is that the Conservatives are transphobic bigots who haven't done enough to protect trans people's rights. They also say the Conservatives are only pushing back on this now in a desperate attempt to win votes from "bigots", and there is probably some truth in that, to be honest.
But delve into the detail of any YouGov poll, read the comments under any article about this stuff, ask any random person what they think about JK Rowling and you will see that there is a huge disconnect between what politicians are saying and what most of the public actually thinks, believes and wants.
Parliament by and large thinks (or, more likely, pretends to think) that a woman can have a penis. So does the left wing media.
But the people do not.
I am fairly sure the same is true in Australia. There seems to be a disconnect between what politicians and the media are saying, and what Australian people are actually saying in, for example, polls on this issue.
And with the polls, you have to read between the lines. You have to read them in the context of the fact that people think that not believing a trans woman is a woman is unkind and transphobic, so they don't want to say that. But if you see a poll where the 90% of respondents have said that they believe a trans woman is a woman and then 70% of the same group have said that they don't agree that trans women should be competing in women's sports or allowed to join women's rape crisis groups, it means they don't actually believe trans women are women and are only saying they do because they know that this is what they are supposed to say. If you actually believed a trans woman was a woman, you could have no logical objection to a trans woman competing in women's sports, because there would be no difference between the trans woman and the female athletes.
Ultimately, I think that we are where we are because most of the political establishment (including politicians, the public sector and the media) is ideologically captured. But most of the population is not, and at some point the the chasm between the establishment and the people is going to grow so vast and so wide that this whole thing is going to fall down into it.
So keep on having those conversations. Keep on plugging away at the people you know. That's what I'm doing. Feed people's ever growing suspicions that the emperor is stark bollock naked with water and sunlight.