Apologies if I'm reading the question wrong, I've read it twice, but I want to stick my two pennies worth in here.
I am autistic, and DS is autistic, and we avoid communal toilets like the plague because there is a constant ringing of the hand dryers, flushing, people gathering in them having a good chin wag, sinks running, soap dispensers creaking etc. There is so much overwhelm in those toilets that I have actually just wet myself before because the anxiety of using those toilets forces me to withhold until there's leakage.
Accessible toilets IMO absolutely need to be separate provision from the rest.
From a carers perspective too, I will probably always need to assist my son in some way. I will need to be there to help or instruct to wipe, and guide him to wash his hands, and be there for him if he gets overwhelmed from the water or noise within a self contained unit as can occasionally happen.
For people who do caring for a living, especially assisted living support workers who's job means that they have to support autonomy in and out of the house, they will also need to support their service users, and there isn't always an ideal ratio of male and female staff to provide same-sex intimate care.
Carers for our elderly, whether employed or family also need to be able to go into the same cubicles. If some lady is taking her dad with dementia out, or some man is taking his wife in a wheelchair out, they deserve a spacious enclosed space to provide that care.
It's just not possible from a disability perspective to keep things single sex without further restricting accessibility.