If there's such a thing as being trangender then there is obviously such a thing as gender in the first place and it is not just a social construct.
"Gender is a social construct" and "gender exists" are not inconsistent. If something's a social construct then it obviously exists. Money, the state, capitalism, countries are all social constructs, but that doesn't mean those things don't exist. Gender being a social construct means it's possible that gender could not exist, but at this present point in time, it obviously does.
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