This link from Language Log shows how China is becoming more progressive than we are with their bathrooms. For the life of me, I can't understand why people here are so worried about people with gender changes using the other bathrooms. What on earth could happen?
Fear. Fear that they may see something. Fear that they may be approached. Fear that they will be attracted by someone or something. Fearing the same things for their children. They need strict separation to keep that fear at bay. We may think it's stupid, but it all comes back to fear about trying to maintain who they think they are and should be.
I don't think it is fear. I think it's far worse - hate. I have long felt that in words like homophobia and Islamaphobia the "-phobia" isn't appropriate. These words don't really mean a fear of something they mean an unthinking hatred of it.
Some people just hate anything and anyone that doesn't fit into their own worldview - be that political, religious or whatever.
I'm not sure we have a general suffix to express "hatred of" but "phobia" doesn't fit the bill for me.
"No man but a blockhead ever wrote except for money." Samuel Johnson.