Okay this is all getting blown out of proportion. Years ago washrooms were used for 2 purposes: 
1. you had to take a dump or 
2 you had to take a pee. 
And women to their own washrooms, men the same. 

What happened? The perverts that is what happened. And everyone knows it was men's washrooms. Several years ago I was doing my business in the toilet and some pervert came in and went into the stall beside mine. His hands appeared under the stall making hand signals and he passed a piece of paper over that said "I want to be your friend".  I grabbed the paper and wrote on it "let me see your face". The perv poked his head under the stall wall and I gave it the hardest stomp I could followed by a number of quick boots. Problem fixed.

So - men to the men's washroom, women to the women's washroom and pervs to the psychiatrist.