I support people who experience gender finding their own new language to name their feelings. It is not for me to impose words for their feelings onto them, any more than it is for them to impose new meanings on the words we already used for sex.
It just needs to be different to the pre-existing language of sex.
Because as you can see, using the same words to mean different things is distressing trans people who believe their gender should entitle them to be treated as the opposite sex simply because of a coincidence of naming, and also distresses people who do not identify as a particular gender but nevertheless are finding people assume they do simply because of the name of their sex.
The latter is especially pernicious for women (in the sex based meaning of the word) since the gender associations of "woman" are often infantilsing, trivialising, over sexual or otherwise offensive or belittling. This is why many women (in the sex based meaning) do not recognise anything of themselves and their lives as women in the gender identity expression of trans women.
Yes, different language for different things would be fairer all round.
Just imagine, if only the genderist community had embraced their gender as additive to rather than exclusive of sex this whole argument and all the distress it causes need never have happened!