It's probably worth pointing out here that the LGB Alliance doesn't just push anti-trans positions, although they seem to exist mainly to do that. They also push homophobia, with directors and other principals opposing legal same-sex marriage, recognition of lesbians and gay people as members of marginalized minorities deserving of human-rights protections, etc.
I was in contact with University of Sussex students during the campus protests, and many of them (including many lesbians) opposed Stock's presence on the faculty not just because of her blatant transphobia, but her support for the very homophobic LGB Alliance.
I can feel Sussex students' eyes rolling as Stock tries to spearhead a movement for lesbians.