That's a good question. In fact, I think just yesterday on reddit the front page had a photo of a sign at a public bath in China saying something along the lines of "No homosexual men allowed", with top comments hypothesizing it was probably more about banning unwanted or public sex acts than homophobia itself.

I assert that this kind of gender segregation is usually about deterring sexualization (and even sexual violence). This is the case for spas, locker rooms, toilets, or even more general places like gyms. My basic position is that being able to deter unwanted sexualization is a useful goal for many reasons, but that's a rudimentary attempt to solve it. At best, I'd say it's a coping mechanism which should be understood as such. So I don't believe they must immediately be abolished, that might be utopian, we need to begin mainstreaming a culture that would enable these sexist institutions to be abolished.

But ultimately:

• They're a product of heteronormativity. Obviously there are plenty of people attracted to the same gender who won't be deterred by this.
• They're a product of normalized sexual abuse in culture. There's a "common sense" that if you put men and women in the same room in a state of undress, then abuse will happen. But we know that's not some ultimate "human nature"! It's a result of culture and social structure. Consider nudist groups and nudist society as a direct counterpoint to the cultural sexualization of nudity.