I'd imagine how it would work is like this: Say a a man is reported to be hanging round inside the ladies loos or changing rooms but when the police are called he claims to be a woman. The police look him up and establish that he's, for example, a registered sex offender. This automatically disqualifies him from declaring himself a woman so the police arrest him.
It would mean, I'd guess, that anyone convicted of sex or violent crimes would not be entitled to self identify.
Trouble with all this is that, not having any idea about some random man's record, women and girls are unlikely to challenge this theoretical man in the first place for fear of being branded a bigot. Also there's the truth that female socialization deters most women and girls from forcing a confrontation. If we're scared of someone we tend to go quiet.
Plus we know that only a very small proportion of sexual assaults and rapes end up in court, let alone with a conviction. The fact that someone isn't on police records doesn't mean they don't pose a risk.
I don't think anything will be acceptable short of a simple rule that you use the facilities that correspond with your sex. That's essentially what we've always had, and transgender individuals who genuinely pass as the opposite sex have been able to break the rules. Given that the only transwomen I've ever seen who look convincing are very petite gay men that works fine. I have not yet seen a sex offender who claims to identify as a woman who doesn't look entirely male, though of course the same is true of transwomen in general.
I can't think of any way both women and the mishmash of identities that travel under the trans umbrella can get what they want. We don't want them in our spaces whereas they won't be satisfied with anything less than full validation.