Sex offenders have never been much for following the law. Why would this kind of law change the outcome?
Do you really not understand?
Because men (in the original sex-based meaning of the word) commit the vast majority of sex crimes. And many men fetishise women's privacy and the things they do in woman-only spaces. Such men are motivated sexually to get into those spaces. Not every man (original sex-based meaning of the word) who wants to get into women's spaces is motivated sexually - some simply feel they are happier and safer there and believe their desires/needs in the matter are more important than the desires/needs of women not to have men in their spaces - not not zero men either. A long way from zero.
If men who claim they are women are allowed to freely enter female spaces, no man in a female space can be challenged, because any man (original sex-based meaning of the word) can make that claim and who is to say he is lying? Not to mention that men who, as far as anyone can tell, genuinely do claim to be women are just as likely, statistically it even seems more likely, to be sex offenders as other men.
But if men are known to be not freely allowed to enter women's spaces, any who are there can be robustly challenged. And that means women's spaces are safer than they are if we have to accept the presence of men there.
It's like locking your door. Thieves gonna thieve, but they get to theive less often the fewer opportunities they get.
And that's without even starting on the desensitisation and escalation element, whereby the transgressive action loses its thrill over time and has to be taken further.
I have a question for you. Do you genuinely believe that the fundamental difference between men and women is not that men have male bodies and women have female bodies, but that women have womanny minds which are sinply mentally different to the manny minds of men? If not, what do you think.the difference is? Why do we even think some humans are "men" and some are "women" at all?