it infuriates me when people use it to bash the Labour Party, as the other Parties are by no means deeply committed to women's rights and I think the Labour Party still stands as the most committed to achieving equality
The difference is that there has always been a part of the Conservative Party that believes that women should be in the home and that the only acceptable way to live is as part of a heterosexual married couple with 2.4 children, nominally C of E even if you don't go to church - the British version of 'Kinder, Kuche, Kirche'.
The Labour Party was supposed to be accepting of secularists and feminists.
However, now, according to LM, Owen Jones and Jeremy Corbyn, it's fine to question the existence of God, but it's beyond the pale to say that there is no such thing as innate male or female gender, and that, not having souls, it is impossible to be born into the wrong body. If you ask somebody what exactly they mean when they say they have a female gender, you aren't a feminist, you are transphobic.
While as a government they are all over the place, as a party the Conservatives sidestep a lot of trans issues because they don't really do equality policy. You might not agree with their policy on AWS but it does have the the advantage of being based on a logical argument.
The current Labour opinion that there should be AWS, but that it's not possible to objectively define the set of people who are women, is absolutely bonkers.