I think the direction we should go in is not to separate genders, but unify them. For example, there shouldn't be separate bathrooms or parking spaces. The more you make the separation, the more divided a society becomes. Just look at many muslim socities like Arabic countries where almost everything is separated.

Now, I am a male, but many females, including my partner, actually advance this point of view. Also look at more equal socities like in Nordic countries, and you'll see that there's much less separation than in countries with more gender inequality.

Of course, we can argue cause and effect and what not, but I still stand by the opinion that separation also has an effect on gender equality, not only the other way round.