The answer is, of course, that "we" don't lump them together; the group as a whole has decided to band together because the persecution and opression they suffer is in many ways shared, and often the kind of person who would persecute one of the groups would persecute all of them. But it's not "anti-trans" or "anti-LGBT" to ask this question.
(Consider "Asian-American", which is more a political/activist construct than anything else, given that "Asian" describes a bunch of different groups, some of which may not have all that much in common culturally or even politically.)
The organization in question may also be anti-trans (or anti-LGBT as a whole), but that's... a separate issue?
This particular group was formed to combat the notion of LGBT identity. So it isn't unreasonable to class it as anti-LGBT, in addition to also holding more specifically anti-T positions.
That's not dishonest, that's a strategic show of strength.
I'm not LGBT, but I do personally know LGB people who don't like the Ts being lumped in with them. They aren't anti-trans by any means, but they see it as a different thing that tends to distract from the LGB and causes more strife. I also know LGB people who share your philosophy and are perfectly happy to have the Ts onboard.
I'm just explaining my POV as an outsider.