I'm not saying they are unrelated. Gender is how culture responds to sex. A trans woman's sex is male, but her gender is female in cultures that include trans as a gender category.

This is not a new thing. Many cultures have had ways for men to live as women and vice versa: their sex did not change, but their gender did. If I remember correctly, there was a female pharaoh who ruled as a man.

PS: Hatshepsut