I wonder how these responses would have differed if they had simplified the questions to something like: “If you were in a room with 100 people in it, how many would you expect to be X, excluding yourself?”
May have better reflected actual experience rather than general 'perception'
During Michael Bloomberg's brief presidential campaign, multiple reporters thought it was a plausible claim that he had spent over a million dollars per American (https://www.politifact.com/factchecks/2020/mar/06/msnbc/bad-...). This requires both impressive innumeracy and a total absence of common sense.
The most obvious point is, how do you tell someone you met is transgender ? The question itself is pretty weird IMHO.
It would also be interesting to see how many gay people the Americans responding to the pew survey reported to have met.
All in all, these survey are about what people think, it seems pretty hard to come up with control numbers, or validate a methodology as much better than another in meaningful ways. At most we could have different surveys from different groups converging toward the same numbers.