"A lesbian who dates a trans woman would not be considered lesbian, because of the genitalia of their partner"

Correct, you'll find that this is the case for most people when you get offline and into the real world. I don't know a single straight guy who'd ever enter a sexual relationship with anyone with a penis, and the same doubly goes for any Lesbian I've met. The inverse is also true with regards to gay men and trans men, in fact, Lesbian friends have expressed more of an interest in more androgynous trans men than any trans woman.

It's called a sexuality for a reason after all, if the sex don't match the perceived gender then most people aren't going to be interested at all, a fact many people in a certain group seem to struggle with online recently.