In the same way that refusing to date someone because they're black is racist, refusing to date a trans woman solely because she's trans is transphobic.
You're lumping some ideas together there. I wonder if there are many black women who are upset at the idea that members of, for example, the BNP won't "date" them.
I don't know if you actually know any black women, but no woman I know is so lacking in self-respect that she wants a white racist, who doesn't see her as a fully equal human being, sticking his penis in her, and then saying "I'm not racist- I have a black girlfriend". Nor do they want to have mixed race children with a man who will never be on his kids' side when those children experience racism growing up. In fact, avoiding that type of man is more of an issue, because some racist men get off on the idea of fetishising and fucking black women. There is an entire sort of porn devoted to it.
There are also racist white women who fetishise about fucking black men. In my own experience though, straight black men are just like straight white men- they don't seem to care nearly as much as women do about whether the person they're having sex with tonight respects them. Nor do they worry that racist sexual partners will pressure them into sexual acts they find too extreme.
So what is it about "trans women" that means they want to be dated by women who don't want to date "trans women"? Why are you raising the subject of racism when they're behaving nothing like black women?!
Actually, let's not be coy here. "Date"? Are these "trans women" really upset that they're not being asked out to the cinema? Or is it that they are truly desperate to go to an Italian restaurant?
No, they're angry that some women have looked at them and thought, "I could never find these people sexually attractive. I would not feel sexual excitement and arousal. My pulse rate would only increase in panic. I would not gasp in excitement as we undressed each other. My vagina would not lubricate, it would not experience tenting (the internal equivalent of a male erection- look it up), and no matter how I closed my eyes and pretended it was someone else doing it, I would never ever approach having an orgasm myself. I do not want to spend an evening getting that person to experience sexual satisfaction, with my hands, mouth or vagina, and I certainly don't want to risk pregnancy".
How many sexual encounters does a lesbian have to have with a "trans woman" before she gets awarded a lifetime Not a Transphobe Badge and can get on with pursuing mutually fulfilling sexual relationships with women who make her mouth go dry?