Although poststructuralism denies the existence of gender per se, the moral branch of the movement preaches that a person *is* the gender they imagine themselves to be, roughly: "Gender is a social construct, however if you feel like identifying with one social construct over another, go right ahead." Don't fret over questions such as "Which construct is the essential construct that I have to identify with to truly 'feel feminine'?" The crudity of language will obscure these difficulties—just say "I feel like a woman" and we will assume we all know the monolithic 'feeling' referred to.
Essentially a new notation is being proposed, and I don't object to that in principle, but I'm not sure why new categories haven't been introduced. Its one thing to say sex and gender are not the same, one belonging to physical description and the other belonging to behavioral description, but why feel the need to use the physical description for a behavioral description? Why not just say "I feel feminine"—? I don't give a **** either way, but I will be interested to see the response when white people start saying "I feel black, ergo..." Or someone says "I feel like a lion, ergo..." Etc.
You aren't a sexist (not for this at least, I don't know much other about you), you just don't accept their notation.