"Gender" is a term associated with grammar. It has no relevance to persons. The word "transgender" is meaningless when dealing with words and even more idiotic when attempts are made to use it in referring to the sex of males and females.
One might try to use the word "transexual" but that is just as ridiculous unless the X chromosomes in the human body could be changed into Y chromosomes or vice versa.
The correct terms for describing a male thinking he is a female or a female thinking she is a male include "pervert," "insane," "batcrap crazy," "liar," "Demonicrat.".
The correct term is, “transvestite”, or “cross-dresser”.
You are correct about gender being a grammatical term, and that nobody can transform their sex.
It’s in the chromosomes, which cannot be changed from one sex to the other.
That’s science.
We used to call dudes in women’s clothing “transvestites.”
If someone went whole hog they had a “sex-change operation” that didn’t change their sex, it just mangled their genitals.
Ding ding ding! We have a winner!
Fowler (Fowler’s Modern English Usage) describes the misuse of gender as a jocularity or a blunder.
Besides the term gender used in grammar, I would also allow for the continuation of the long-standing use of the term gender in electronics (male and female connectiors, gender changers).