Some excellent posts on this page.
AussieNanna, I agree that there should be a separate category for transpeople. To me, this would make far more sense than the idea that 'transwomen are women'. It would mean that transpeople can live however they like, but not 'become' the other sex, as this is impossible.
We should continue to have areas segregated by sex where this is necessary for the safety of women (eg prisons, refuges and hospitals) and transpeople should access the ones appropriate to their sex, unless there is separate 'trans' provision. I also think it is important to ensure that such trans provision should not be created at the expense of provision for women (ie it should be funded separately and not be the more modern/better equipped alternative to women's provision that would advantage those who can access it by self identifying as female).
Where health is concerned, I also feel that steps should be taken to ensure that money is not syphoned off things like HRT and other gynaecological issues (eg endometriosis) to pay for transitioning hormones and surgery. I understand that this is currently happening.
This is not said because of 'transphobia', but because of feminism. Yet again, male 'women' are prioritised over actual women, and it is a disgrace.