Seems silly in this day & age that we should need to explain the difference between men and women & which restroom each should use… or shouldn’t use. I cannot imagine any person holding a doctorate having such a problem in making such distinctions.
Be that as it may, I actually have a very simple solution, which might have additional advantages. Actually, the solution has been in use for over 40 years, on planes.
On airlines, there is no gender distinction. Each room is used for both, but only 1 person at a time. The beauty of this is that there is no need to wait for the men’s or women’s room. Each is used in turn without regard to gender.
I noticed in many public places, such as theaters, the women’s lines were always, without exception longer. If it was 1 person per facility, gender wouldn’t matter. It would be one line. And, of course, if a man chose to lie to himself and others, no problems. He’s by himself, anyway. Moreover, no worries of a man walking into a ladies room. (Oddly, I don’t recall hearing of problems or women going into men’s rooms.)
I suppose people could take tickets and wait their turn. I don’t know.
Of course there are real problems. Some facilities would have to accommodate handicapped. It would mean drastic reconstruction. In some some cases it might not even be practical. On the other hand, it might be as simple as changing the signs on the doors.
Then again, some people just don’t want solutions. They prefer fighting over it. Don’t have any idea why men want to use ladies rooms. Maybe they were just never properly taught. On the other hand, maybe they were improperly taught in the fantastic public schools. I mean, if the teachers don’t know the difference, how can we expect the kids to know any better?