Here's an alternative:
1. Biological sex is merely one's reproductive configuration.
2. Stop labeling people with regard to "gender". Doing that is a step _backwards_. Why do we need these labels???
3. Accept that some people have a compulsion to "identify" as the other sex. That disorder needs to be accepted, and people with that need to be treated with respect and compassion: if dressing "as the opposite sex" alleviates their anxiety, support that.
4. Accept that a tiny percent of the population have ambiguous biological sex. Those edge cases do not invalidate any of the above.
If someone with male reproductive biology "feels like a woman", what does that mean? Just because you feel like you are stereotypically feminine in some ways does not "make you a woman", or nor does feeling like you are stereotypically masculine in some ways "make you a man". You are just _you_ - and that's okay.
This cultural need - something that has arisen recently - to "identify" as this and that, is an enormous cultural regression. Instead of treating traits as one's "identity", we should treat them as mere adjectives:
Instead of "I identify as a woman" could be "I tend to relate to traditionally feminine things". See the difference? The former puts you in a box; the latter leave you free to be whoever you choose to be.