OP, I'm guessing you have been advised/brainwashed by university that everyone identifies as something which in the real world isn't true, whereas everyone does have the sex they were born with.
if you do things with gender then first you exclude a tranche of people who think gender is made up regressive nonsense and also on other surveys you could come up with things such as '0.001% of men have been pregnant'. Your data will be muddy.
Unless your survey is to do with gender issues, i would suggest you either stick to sex if relevant, or have both a sex and a gender question, but the gender question should have 'no gender' in the same way a faith question would have a 'no faith' answer.