There is no bouncer in front of the McDonald's bathroom. There is no need for words, magic or otherwise.
Fiat self-ID as public policy doesn't solve this problem. Indeed, it makes this problem worse. In some cases, it ends up criminalizing people's attempts to police these spaces by social pressure, which has been the customary first line of defense for generations.
In the case of Jessica Yaniv and others like him, we've seen this harassment of women, and the chilling effect on social recourse, even in venues that do have some sort of official gatekeeper. Because, by law, fiat self-ID must trump the "bouncer's" own judgement. If the bouncer acts otherwise, it is the bouncer that is committing the crime, not the predator.
The good news is, the law does not
necessarily have to come down on the side of gender segregation and fiat self-ID. It can just as easily come down on the side of sex segregation and social pressure. The bad news is, there's a lot of people who want you to believe that the law must side with gender, and to accept their policy proposals for such laws.
It would be interesting to see your complete argument* about what you believe the law
should say, and why you believe that.
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* For me a complete argument consists of three things, presented together as a unitary whole: Your premises, your conclusions, and your reasoning connecting the former with the latter.