That’s the crux of it, yes. But trans women and activists would say that they are women (the TWAW movement) so actual lesbians are just a bunch of bigoted transphobes.
Thinly disguised misogyny in my humble opinion.
If you really want to go down a rabbit hole, google the Allison Bailey case vs Garden Chambers/Stonewall and also the Gay and Lesbian Alliance. You might be down there a while though.