I don't see the elimination of gender-segregated washrooms as a step forward. For one thing, women don't pee on the floor, and nearly always flush. If I'm fixing my makeup in the mirror, I really dont want a guy standing behind me, leering at me, or telling me to hurry up because he wants to wash his hands. Plus, I don't think we can really count on guys not to peek
Of course people should use the restroom they think is appropriate for them to use, rather than have arbitrary standards applied to them.