OK, here's where I sometimes come unstuck, as someone who was a liberal feminist until about a year ago and is still working and thinking through this stuff (with the help of this board):
I accept the importance of biology. TW are not biological women. Sex and gender are different and shouldn't be conflated.
I believe that biology is at the root of sexism. We are oppressed because of our sex and because of gendered expectations and limitations heaped upon us (and on men) from an early age based on our sex.
I'm on board with the need to distinguish between biological women and trans women in certain circumstances, and to reserve certain spaces for biological women.
I agree that we need to fight the erasure of the word 'woman' and of words describing our sexed bodies. We need to be able to talk about menstruation, breasts, pregnancy, menopause etc. as women's issues, because (even if, for the sake of argument, we accept that TWAW are women and TMAM) they are issues that overwhelmingly affect and unite us as women. We need to continue to exist as a sex class, and we need to retain the ability to organise politically to fight oppression.
What I'm unsure about is this: Why is it necessary to always and exclusively define the word 'woman' based on sex? 'Woman' is a word that carries multiple layers of meaning, including aspects that relate to gender (by which, again, I mean the expectations and limitations placed on us based on our sex). It is perfectly normal to me, as a linguist, for words to have multiple, sometimes overlapping, meanings depending on context. I know that this will sound like 'ceding language' to some, but honestly, I think 'woman' and 'man' have always had gender-related meanings as well as sex-based ones. If you'd asked someone in the 15th century to define 'woman', I'm sure you would have got all kinds of shitty gender stereotypes as well as biological facts.
Basically, I don't know if arguing about the definition of the word 'woman' is all that constructive. In the circumstances where you need to limit its meaning to biology, surely you need to specify that anyway, given the scope for confusion and equivocation if you don't? Why can't we say that TWAW, in a certain sense of the word?