Aw hell no dog! This won't fly.
In emergency's it can happen. Think movie-theaters with a break in a long film. Girls will use the men's bathroom because the line in front of the ladies is just not manageable. And that's totally fine but still, the only way a woman enters then is with a lot of apologies and looking at the floor.
This shouldn't be common practice. Women don't feel at leisure when they have to go to the men's bathroom. Plus, men tend to leave bigger messes on pots - especially in schools. I doubt women would find that pleasant...
The Doctor will see you now Promoting Lesbianism -->