If your filling out a form (non-medical) and they ask for your gender/sex with options of "male" "female" and "other". If you're cis, you select your birth sex. If your not cis, you have to select something else.

Many trans people have recognized their biological sex outside of medical forms (including Blair White and Buck Angel), knowing your biological sex is not gender identity. You need proof that the person admitting being female/male is a hardcore genderist and is indeed referring to gender identity and absolutely not biological sex when using words for biological sex. As you define male and female as gender identities then you calling yourself the word you use for a gender identity can be used as proof of you yourself having a gender identity but it doesn't prove any of that for those who don't share your genderfied definitions. That would be like if an American speaking English would call a bottle of wine a "gift" and the German police would arrest the American for admitting to giving away poison as gift is the German word for poison. Using a certain letter combination can only be proof of having a gender identity if that letter combination is the letter combination the person personally uses to refer to gender identity, otherwise the person is speaking about something else.

Ok. Someone without a gender identity is not a man or woman.

As you define man and woman as gender identities someone without a gender identity would have neither of gender identities you refer to, so yes, that is the most consistent/respectful stance a genderist can take. I think people who define man and woman as gender identities are morally obligated to never call anyone a man or a woman unless they have proof the person has the gender identity referred to as we shouldn’t make assumptions about people's minds.