To the posters who are saying that the number of murdered women are not statistically significant (!) let's add in some other categories:
rape/indecent exposure/sexual harassment/sexual assault/stalking/bodily assault aimed at women. In addition to which the number of low-level, misogynist micro-aggressions such as comments that women endure.
I have in my life been subject to being followed home by a 'person' with their penis flapping at me, had my breasts grabbed and twisted on three separate occasions, had men masturbating near me in a cinema and on the tube, been intimidated by male taxi drivers making 'suggestive' remarks. As have many, many women I know - as I've mentioned before read 'Everyday Sexism' by Laura Bates.
I and many of my fellow women have not reported these as crimes, for many of us it's just a fact of life. Single-sex spaces be they ones we 'choose' to use, such as public toilets, single-sex saunas, gym facilities and those women are forced into because of circumstance such as refuges, homeless hostels and prisons, are places where women are, if nothing else, safe from these kinds of events.
No woman has ever done this to me or the women I know, be they lesbian or trans men, only people with penises.
And even had none of these things ever happened to me or people I know, I am aware enough that they do happen and frequently to other women. I have not been subject to FGM but know that women should be protected from it.
So the posters who think single-sex spaces are no big deal, bully for you, I'm glad you and no-one you care for has been subject to the forms of literal violence many others have been. This does not give you the right to sacrifice other womens' safety or dismiss their concerns. Nor does it give you the right to exclude women whose beliefs make it impossible to enter non-segregated spaces, so may then be unable to access a number of public spaces.