This isn't rhetoric, the LGB Alliance isn't some group that just happens to not focus on T of LGBT. They're a group that wants the T dropped from LGBT, that believes, advocates for, and fights for legislation that defines trans men as women and vice versa. They were literally established in opposition to LGBT groups supporting trans people and still are.
There is no gaslighting whatsoever, one of the co-founders literally, somewhat famously, broke down in court when backed into a logical corner about whether trans women were lesbians. Even if you take the naive definition of "transphobia" where there must be actual fear it still holds up.
Of course they don't say their beliefs are transphobic. That's the real rhetoric -- because they're happy to tell you that they think that trans women are men who pretend to be women like that doesn't invalidate the very core definition of what it means to be trans.
This group would run into no trouble whatsoever had they had no stance at all about trans people and just said that they preferred to focus on the sexuality rather than gender issues.