Maybe, but LGB Alliance is so socially conservative and anti-sex to begin with that they would also repudiate that term anyway.
"Queer" in my mind fits as a nice amalgam for all of the sexual orientations that are targeted by the Right. You could still use specifics if you want to define particular subgroups, but "queer" has the advantage of implying that the opposition to their humanity is based on them being sexual "outlaws" & not "normal" cis folk.
Also, just as it is possible for White folks to be antiracist/socialist and people of color to support White Supremacy, it is also just as possible for non-cis folk to be very socially & sexually conservative if not reactionary, and for "cis" folk to be radically supportive of queer/sex radical thought.
@darkwiiplayer Choosing and reclaiming words won't stop the hate, but can make it more difficult to spread it.
It's kind of hard to get someone upset by calling them a name if they embrace it.