Slavoj Zizek: “As soon as you flush the toilet, you’re in the middle of ideology.”
If you look at Western history from the Roman Empire to the Middle ages, men and women washed together in State run communal bathhouses. There were also communal latrines. The pendulum swung and during the Protestant Reformation, there was a washing moratorium (long story). By the mid-19th Century, the pendulum swung again and with Victorian era values and advances in medical technology, personal hygiene became associated with Christian purity, morality and respectability. Sex segregated bathrooms arose. This rise was closely aligned with the Victorian idea that women were emotionally and physically vulnerable. It was during this time that when the fear of bodily substances took off and moved into the late 19th and early 20th century. Le Corbusier's iconic Villa Savoye exemplified how users could disown their mortal flesh and it's by-product through concealment.
I have to say, I'm really having a laugh at most of these posts and not for the same reasons most of you are. Single occupancy all-gender toilets as unique? I've lived abroad and many, many places are perfectly comfortable not just with a single occupancy all gender arraignment but many with a multi-occupant all gender toilet rooms. Up-scale restaurants in Hong Kong? Abso-freaking-lutly. Stall walls simply go from floor to ceiling. Lavs are shared.
This is current thinking in many academic buildings currently being designed in the U.S. and many corporate facilities in progressive areas. The tv show Allie McBeal introduced this to Americans a long time ago.
President Obama declared Title IX has protections guaranteeing trans individuals access to sex segregated toilets that align with their identity. The fundies freaked and most of the hysteria is closely tied to this event. The current occupant of the white house overturned the protections.
Fear is where the pendulum is at.