There are two problems with this.
The first being that there are changes happening under the Tories on this issue. Perhaps more under BJ than Truss, but they have been happening.
But it's also a statement that takes no consideration around how this ideology has operated. Gender ideology exploded onto the scene some 10 years ago, in different countries, largely without regard to what political party was in power.
It operated by capturing officials and institutions quietly, at a low level, and by convincing citizens ad political leaders that it was just another element of gay rights and was also medically and scientifically supported. Articles were published in popular, trusted sources like National Geographic, Scientific American, etc, and major media sources like the Guardian, BBC, CBC, hopped right on board.
The UK, and really England, has actually been unique in stepping back and putting the brakes on the policy element. Unlike countries like Canada, NZ, Scotland, even the US. We don't know for sure, but based o their response there is every reason to think if Labour had been in, the UK would now have laws like Canada, where a women's shelter cannot legally refuse to admit a woman with a penis.
That still, today, seems to be the approach Labour is taking.They have not even allowed open discussion in the party on the issue, which has been disturbing to many even apart from the issue of gender ideology itself. (What else might they not discuss even if their MPs and members are concerned about it.)
No one who makes this argument you have made has ever been able to claim that it would have been different under Labour, because we all know that it would not, it would be worse. Why this exploded as an international issue that captured s many institutions is well worth considering, but it was not caused by the Conservative Party.