I have never seen 'men's' and 'gender neutral'. What I have seen is the reverse, which some places have implemented to reduce queues. I.e., there's a ladies and a gender neutral.

Men who urinate standing up (which is not all men, not even all cis men) take less time than women to use the facilities so having women's and gender neutral makes sense, especially as women will just invade the men's room anyway when the lines get long enough ;).

One of the conventions I go to designates one set of restrooms as gender neutral during the convention, with the blessing of the hotel. I have to admit I take shameless advantage of it...enough people of both sexes are uncomfortable with gender neutral multi-stall bathrooms that the lines are always short for that one ;).