I dislike the language around this to the point where I disagree with the people I agree with! 'Liberal' is copying American parlance and replacing our 'lefty' or 'socialist' or the more politically value-laden 'progressive'. It doesn't mean Liberal as in Liberal Democrat Party but aligns more with Labour Party and perhaps others such as Green Party,
'Gender critical' is an obscure term in the context in which it is used and I am not it. And it's not 'gender ideology' or 'genderism' but 'gender identity ideology.' 'Gender' has been redefined by various Humpty Dumptys from meaning 'sex' to some social theory thing, to gender identity which is a personal notion or choice. (Terms are bandied about such as 'Gender Theory'.)
The whole thing is fraught with contradictions and impossibilities and it It is won or lost on the use of language: How can you state 'A transwoman is a man'? A man is a man. If he's a man why the word 'woman' (as part of a compound) to denote him, while stating he's a man?
Again, I don't agree with the often heard statement that the speaker doesn't care if a man wears women's clothes. Well, that's what a certain Eddie, for example, has done. The problem is that it doesn't stop there. Another is that when men do it, our media and eager men and women all over the place rush to call him a woman. Why the rush to deference?
And the practical effect of all that is that we end up not knowing who is who or who is a man and who is a woman and therefore who is in our women's toilets, changing rooms, sports, lesbian groups, rape crisis services, hospital beds or indeed whether the doctor treating us is a man or a woman, or how or to whom to apply various laws, etc, etc. We think we can tell and in many cases we can but even though I may be convinced in my own mind that I can always tell, it isn't possible.