I really don't understand this question of why they aren't doing anything if they really believe that. That feels very naive to me.
The situation on this issue has been changing really rapidly over the last five years. It was for the first several years of that, and before also I suspect, activist driven. Almost everyone was swayed by their influence including all of the political parties, in a general kind of way. And many different kinds of institutions and organizations, schools, prisons, NGOs, the police, even the civil service, were very much affected by the activist groups that began to push these ideas. Not least SW because of its huge influence and reputation, like the Vatican of the secular humanist Labour voting crowd.
And political parties across the board started to craft legislation on this basis. Right up until they started to get all kinds of pushback, largely though not exclusively from women. And despite all the attempts of activists to shut down any disagreement or attempts to discuss the issue.
And all along, when it was only a few people in politics listening, they tended to be Tories, not Labour or LibDem or Green. Similarly the political figures who really went to bat. Worse, the LP, LibDems, and Greens went all out trying to shut down differening points of view, right up to trying to kick them out of their parties.
It's only in the last month, or last few weeks, that there has finally been a real hard political statament at the highest level by Conservatives, culminated in the last few days with these statements by BJ. There is every reason to think that this represents a significant consensus by the party members overall, and what that means is they are now in a position to begin working to change some of these things that have gone through on the sly all over the place, largely due to bad advice from lobby organisations.
It's now possible to wield political influence on this given the weight of perspective in both the CP and among the public, and we should expect to start to see actual changes and hold them to that expectation.
If Labour were in, right now there would be self id and psychologists would not be allowed to offer kids in therapy anything but affirmation, and SW would still be offering their flawed indoctrination to public and political institutions across the country, and they would be actively suppressing any discussion of gender issues.