@Didimum
The fact is women are statistically safer with a transwoman who is a stranger in a changing room or a bathroom than they are in their own home with a male-identifying partner or family member.
I'm sure that's true (at least where "male-identifying means actually, you know, male...unless you have evidence that trans men commit domestic abuse at the same rate as natal males?).
But it's not really the point, is it? Sadly women are statistically safer with any male who is a stranger in a changing room or a bathroom than they are in their own home with a male-identifying partner or family member.
So by your logic, we shouldn't bother with sex segregation for safety at all, because statistically, women are more at risk from known males than strange ones. (1)
Unless you happen to have evidence that trans women are statistically less likely to abuse women than other males? (3)
(1) Note of course that underlying this logic is the rather disturbing belief that since female people already suffer high rates of abuse and asault and rarely feel 100% safe anyway, adding a bit more abuse, assault and fear on top doesn't really change anything and is a reasonable cost for trans women to feel validated (2). Furthermore, that although statistically the average woman is more at risk at home, at an individual level the majority (sadly a much smaller majority than it should be, but still the majority) of women are not in fact at risk at home, so for them the public risk that you wish to increase is the more significant. The fact that the cost is all paid by female people and the benefit all accrued to male is apparently not a significant concern, the blanket term of "women" for both obscuring the fact that one specific group of "women" is the winner here and a different, also specific group the loser, and I'm sure its just a happy coincidence that the winners here are male yet again.
(2) I say validated rather than safe deliberately because there are many ways trans women could be made safer without appropriating female resources, so the significant factor in the demand that safety requires the right to be "in with the other women" is not in fact their need for safety (a reasonable need indeed) but their need for validation as women.
(3) A genuine question, does anyone know if trans women less likely to commit domestic abuse than other males? I know the incidence of domestic abuse against trans people is higher (sadly IIRC those AFAB at birth suffer more than those AMAB, but I think AMAB rates are still higher than the general male population) but not whether transitioning affects perpetration.