I personally don't understand the point? Nobody is forcing anyone to date anyone. Yes you might be called transphobic if you refuse to date a trans person and is it okay? No, but who hasn't found themselves called names by a "good guy" who is pissed because "girls always go for assholes."
Whatever really.
You don't want to date a transwoman, don't date one. Would I date a pre-op transwoman? No. Would I date a post-op transwoman? I don't know, does that make me transphobic? Maybe. I personally don't think so but if someone else feels it does they are entitled to that opinion and them believing I am transphobic doesn't impact my life because I know I am 100% supportive of trans people and them getting the rights and protection they deserve.
Trans women are women in my point of view (and yes I know how controversial it is to feel that way on mumsnet) so stating lesbians are female homosexuals aren't actually offensive to me, but it seems like it comes from the point of view that most trans people are self-identified people who act, look and behave like straight men, when most trans people actually transition and take step towards transitioning. I don't see why I would see post-op transwoman as less of a lesbian than I would a "cis"-woman.
I personally wouldn't date a woman who is anti-trans, I won't go to pride holding a banner making a point of it. You don't want to date trans people? Don't. Hold your grounds about it but don't go to pride on a day where people of all orientations are supposed to come together making (trans) people feel unwelcome. It's a really shit way to go about things really.