Like all genders, I would ask them what is “correct.”
If you’re asking about _sex_, however...
in the case of intersex conditions, they arise from a disorder of sexual development which by definition arises by diverging from the typical developmental pathway of one sex or the other. Much the same as someone with a much later and artificial divergence (e.g. hysterectomy), this sex is still their sex despite their intersex condition.
Being born “without genitalia” is still going to be one of these conditions, or the result of some other unspecified trauma or non-sexual-development disorder. They would still be either one sex or the other.
Mosaicism is an interesting case. It would depend on which cells were activating sexual development.
Yes, there is good reason to make a distinction between the terms, just like there’s a good reason to distinguish between “brain” and “soul.”
I don’t have to believe the shahada in order to conduct myself respectfully with a person of the Muslim faith, and I don’t have to believe a female is a man in order to conduct myself respectfully with a trans man.