Why would you expect them to care? They’re all different flavours of liberal progressivism.
Liberals don’t care about group rights they care about individual rights. Liberals don’t see women as class with group interests, they see them as individual people, feminism sees women as a class.
Reform UK might do something about this, I don’t know, but the best you will get from Tories is ‘we are dreadfully sorry that this is happening but to actually do anything about it would be illiberal and unbritish so we mustn’t do that’.
Think of how this looks to your average centre left liberal. They want to free individuals from all social and moral norms which they regard as an oppressive pressure to conform to the wishes of a tyrannical majority. They totally reject conformity.
Now these progressives have already been persuaded that almost all of the meaningful differences between men and women are the result of socialisation and believe that boys can be socialised to be more like girls (wonder where they got that idea from). So when you ask such a person if a person should be treated as the sex they were born or the sex that they would like to be or identify as, what answer do you think you will get? They will obviously tell you that individuals can be whoever they want to be.
That’s why the ideology could spread so quickly, the powers that be agree with its logic and reasoning, because they’re liberal and progressive people. The British establishment is now university educated liberals, the country is no longer run by old aristocratic men with country estates.