Gender identity is a well established scientific term, used in multiple scientific journals and peer-reviewed research.
Sure, to describe an observed phenomenon where someone believes they should have been, or internally really are, the opposite sex. It's a big, unevidenced jump to conclude this means they in reality ARE the opposite sex, and therefore that all hitherto assumptions about what sex is, and what each sex needs and the risks it may face or pose, are wrong (1)
There is, after all, plenty of scientific, peer reviewed literature about named mental states of mind where the subjective perception does not align with objective (or at least consensus) reality.
But that's rather beside the point. Gender identity may be as really real as a real thing can be, but it's not the same thing as sex, and the "accident" (ahem - deliberate manipulation) of language that has happened to land it with the same words as sex are not any sort of basis to claim sex - based rights and privileges.
(1) Except they don't, do they? They say is the one hand humanity has totally misunderstood what a man and a woman are, but on the other humanity miraculously managed to set the single sex things up just right anyway, all we need to do is swap sex for inner gender and it's all ticketyboo, no need to really think about it at all, we'll just take all this for the male women thank you. And no, female bodied people who are no longer the definition of women don't get to redefine themselves, what are you, crazy? You just carry on womaning like you always did, why on earth would entirely denying the basis on which you understood yourself to be a woman change any of that?