Maybe I'm being a Western chauvinist, but it seems to me that this kind of gender segregation is the hallmark of not very nice societies, be it those dominated by religious fundamentalism or in societies where male sexual violence is rampant and implicitly allowed (probably a good bit of overlap in these categories)
The integration of women and men in the public sphere strikes me as an unambiguously good thing, but I suppose opinions can differ.
An integral part of the discussion is about where people perform bodily functions
That isn't the public sphere, unless you live in SF I suppose.