Trans women already use women's facilities, they have to in order to get GRA.
That's not at all true, @Smileifyoucan - it's a myth. How on earth could it be true - how could such a claim ever be evidenced, anyway? And how can it be true, when the Equality Act quite specifically says that women are allowed to have sex segregated spaces, which even a GRA can't force access to (despite the EHRC and the GEO misrepresenting the law - legal advice which they have withdrawn, since, as it was wrong).
And while absolutely, trans people are no more likely to offend than anyone else of their biological sex, they're no less likely to, either. Transwomen sexually offend at standard male rates, and while the vast majority of men don't offend, the vast majority of such offenders are male. Which is why we have sex segregated spaces to begin with.
If sex, not gender identity, detemines risk, why are the feelings of people born with penises seen as more important than the feelings and safety of people born with vaginas? I mean, isn't that a classic example of absolutely blatant sexism? And if not - why not? Why are the feelings of males so desperately sensitive that a small number must be catered to, however much that guarantees harm to a large number of women? Can you explain that, please?