I just returned from my first visit to Israel last week. It was eye opening in many ways. One significant eye opening realization is that many (not all) of their public restrooms are a set of stalls for use by anyone. It didn't matter on the neighborhood or the quality as we found this everywhere. I think the only time I found them separate was when we had to pay to use the public restroom or when the restroom was located in a tourist trap type setting. In those cases, they were separate.
This is a society that is basically controlled by the orthodox and ultra-orthodox Jewish men. These are very conservative men worried about touching women and becoming unclean. They control marriage, they control immigration - they control a lot! So, it's hard for me to believe that they wouldn't use their Knesset power to override the existence of these unisex bathrooms if they saw them as a problem.
I saw women and men going in to these restrooms and using them and then leaving. There was no fear in the women's eyes worried that they would be assaulted by the man in the next stall. Some of these bathrooms were in areas I considered pretty seedy with dirty and broken bathrooms. These people needed to pee, so they did and then moved on with their lives.
As an American, I was incredibly uncomfortable with it. It's weird to me because it's not an every day occurrence for me. Beyond that, there was no issue. I used the restroom and then moved on with my life.
So, two weeks ago I would have said they need to be separate and stay separate. Now that I have personally seen the concept in action in a community that has people from every walk of life from the very secular to the very conservative ultra-orthodox people all living alongside each other, I see that it works. For that reason, I say why not?!