But do you know what proportion of those sexual crimes are against women? As opposed to against other men for example, or indeed against children, or that don't invlove and present victim at all - e.g. pornographic material-related crimes, or revenge porn?[...] I'd also be interested to know if anyone can say, of the sexual crimes against women, how many are against a partner? Or another known person - a friend or a colleague? Or are related to prostitution? Because I don't think it's fair to include those stats when attempting to show how sexual offences by men are somehow likely to occur in public bathrooms against women, were they to be mixed gender spaces.
Sorry for the massive quote, but this attitude is grim. Everything you've listed involves the deliberate assault and/or humiliation of a person who is physically weaker than the perpetrator, or who is, for other reasons, unable to protect themselves.
Whether the perpetrator assaults women, men, or children, they''re forcing themselves on someone because they had the inclination, the opportunity, and the physical capacity.
Whether they assault partners, friends or strangers - the same.
Adult consensual porn isn't illegal, so I imagine pornographic-related-materials convictions relate to possessing images of a violent/non-consensual nature. Revenge porn is the intent to humiliate and demean a partner, again because the perpetrator has the inclination and the opportunity.
Exposing yourself to, harassing and sexually assaulting women in enclosed-but-public spaces (such as toilets and changing rooms) is not in some entirely discrete category of crime. It's like saying 'date rape isn't as bad as being attacked in a dark alleyway by a stranger'. There's a huge crossover amongst all kinds of sexual crimes: inclination (to force yourself upon, assault, scare or humiliate someone), physical capacity (choosing someone who is unable or unlikely to effectively fight you off or hurt you), and opportunity (being in an isolated space together).
Single-sex facilities are about removing or reducing the opportunity. I don't live in a constant state of anxiety about being assaulted - but I'm not in denial, either, and would have no sense of safety being in an isolated or vulnerable setting with the perpetrator of any crimes which demonstrate a desire to hurt, sexually assault or humiliate. These people aren't easily identifiable, but they're invariably male, which is why single sex facilities are a relief to many women.
Insinuating that our fears should be dialled down because, hey, a lot of those sex-offenders actually raped their partners, which is totally different from assaulting strangers, is not going to change anyone's mind. Nor should it: because it's shite.