I don't like using public restrooms either.
To me, there seems something very mentally uncomfortable with standing next to a stranger at the urinal & getting my penis out to take a pee. Therefore I either use the cubicle, or a disabled toilet.
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We, the people on the Autistic Spectrum have a choice.
We can either try to "fit in" with the rest of society, or we can be so egocentric that we can't be bothered.
I choose the actor. I observe NT's. I listen to their socializing. I practice it, so in social situations I can just emulate/mimic what is expected.
It isn't natural for me, but it enables me to "fit in".
It is VERY tiring and draining, but at least we can appear like them even though it is an act. Like being on the stage.
They can't see it is emulation, and so we are accepted.