20th (even late 19th century) public or shared toilet design had no flaws. It recognised biological reality and the different needs of the sexes. At its best it included a full time caretaker attendant of the appropriate sex who attended to the cleanliness of the facilities and to users' needs and safety, and repelled people who should not be admitted (drunks, known drug users, members of shoplifting or pickpocket gangs, people of the wrong sex).
There were quite a lot of them, they were clean and safe, basically perfect, and an admirable use of public money. There should have been a higher ratio of women's to men's, and there should have been more accessible loos. That's all.
Loos in schools, colleges and workplaces also worked.
The provision system wasn't broken, it doesn't need fixing.
Men and transwomen in the men's, women in the women's, transmen in either.
Complete non-tolerance of violent reaction to gender nonconformity.
Complete non-tolerance of breaking the sex-based conventions of decorum.