US or UK, this goes one-way only.
For example, should a student self-identify and dress as Robert E. Lee all hell would break loose. No respecting of personal choice there.
There was an old joke about a black boy who identified as white, and his father beat the living daylights out of him. He said through his tears, “I’ve only been white for five minutes, and already I hate you black folks.” I assume he didn’t go so far as to join the KKK.