I'm not sure if you had this in mind when you said "non-binary", but I also think along the same lines you just noted, that there is a difference between "not binary", and "non-binary". The latter could evoke connotations to the culture wars and gender identity -- though that of course has nothing to do with accessibility (of TUIs, bathrooms might be another matter).
Then again, I'm neither American nor a native English speaker, so I hardly have much authority on this point.
I'm not sure if you had this in mind when you said "non-binary", but I also think along the same lines you just noted, that there is a difference between "not binary", and "non-binary". The latter could evoke connotations to the culture wars and gender identity -- though that of course has nothing to do with accessibility (of TUIs, bathrooms might be another matter).
Then again, I'm neither American nor a native English speaker, so I hardly have much authority on this point.