I suspect they wouldn't , and I don't totally feel comfortable at the idea of public toilets becoming mixed gender.
It depends where it is.
I don't have an issue with transgender people using whatever loo suits them.
They are only a small number of people, not 50% of the human population.
We don't need a special transgender toilet because we already have disabled toilets that are often mixed gender anyway.
It shouldn't even be an issue, IMO.
I don't fancy sharing a public toilet with a bunch of drunken lads, staggering about and throwing up.
It's bad enough when the drunk and weird man sits next to you on the bus and train and I would prefer not to find him in the loo as well.
Transgender isn't the problem, not really.
The problem is finding a bunch of loud mouthed drunken louts in the same public loo.
Sometimes at service stations you get a male cleaner and we accept him.
Mind you, in work the male cleaner is so terrified of women being in there he won't come in and even clean the sink, he runs away looking embarrassed.
Daft it is IMO.
The way he behaves anyone would think we women are dangerous!
It doesn't bother me, I'm in a cubical.
In pubs it depends on the toilets, if they are inside and a bit like home, it doesn't matter.
If it's outside, not keen.
Happy for transgender to use the same loos, happy for male cleaners to clean them, happy to share home type loos mixed gender.
Not happy with totally sharing public loos mixed gender.
Transgender not a problem as far as I'm concerned, might be different if it was open showers in a gym or changing rooms where you strip off after swimming.
I'm shy with other women anyway. ( hate showing my scars very self conscious)
But toilets not an issue with transgender.
I think we have the answer already, where it causes awkwardness use the disabled loo.
Where it could cause a problem and awkwardness, like showers and changing rooms perhaps we need to ask for individual cubicals so you can change in private.
Some pools already have them and both men and women and families use them.