Like in the title. Did it have more to do with gender priviliges ( i.e. women in ancient Rome could not vote or hold political powers and baths were a place of social meetings ) than being distracted due to sexual attraction? Or was it simply because homosexuality in ancient Rome wasn't as common as it is believed ( e.g. common only among aristocrats )?
I do not want to start any political debate here. Asking out of pure curiosity
Disclaimer: not historian, only took a class about women in ancient Rome, which wasn't even a history class.
I think it would be useful to first note how extreme ancient Romans would find the idea of naked women spending time together with other men. Roman wives, in the most traditional and idealized image, were not allowed to even be in contact with other men except their husbands, and the behavior of unmoderated contact with men in public space itself degrades the status of a woman. The risk of adultery, and the loss of the female pudicitia (modesty) was a pervasive fear among ancient Romans. To answer your question directly, in the traditional sense, female sexuality itself was perceived to be attractive to men, and to uphold the sexual status of the women in public baths (and thus indirectly protecting the civil status of their husbands), it was self-evidently necessary to separate the genders in the baths.
Unfortunately I don't know a lot about male homosexuality in ancient Rome; I will not comment a lot on that. From my knowledge, male homosexuality was, as an understatement, much more acceptable than the risk of adultery and the loss of pudicitia, so it might be mostly a difference in severity.