Hang on in there. I reckon this is exactly the sort of action we need to see.
Because most people in the population are not bisexual (or pan sexual, or whatever). Most are heterosexual or homosexual, i.e., there's one precisely one genital set up out of the two possible ones which turns them on.
And the "lesbians ought to accept lady dick or they're bigots" mantra is the point at which the personal becomes the political. Because the instant a reasonably intelligent person generalises the issue to their own life ("hang on, you're telling me that if I don't want to fellate a penis/go down on a vulva - delete according to which one is a turn off for you - I'm a bigot?"), that's the moment the whole carefully constructed pack of cards comes tumbling down. Because it is the point at which 90% of the population realises that no matter how right on it may be to repeat the mantra "TWAW/TMAM", they don't actually believe it. They know that the slogans aren't true.
Of course it's fine and laudable to campaign for transwomen and transmen to go about their lives free from harrassment, having equal access to employment (barring a tiny handful of jobs where biological sex matters), housing, etc. But most people can't make the step to believing "TWAW/TMAM", because they aren't. And sexual attraction (or lack thereof) brings that home in the most immediate, irrefutable way possible.
That's why it's such a threat to TRAs, but at the same time is a battle they can't possibly win.