That is the good thing about groups online - there are generally so many of them that you can pick and choose what kind of community you want to be a part of. I think the understanding you've come to is that that group is probably not the right one for you.
If it were me, I would just leave that group and spend my time contributing to groups that better represent me. I've left quite a few trans related groups in the past for all kinds of reasons. Though it's always tempting to debate publicly when people are talking out of their butts, it's better in most cases to just drop it and move on to greener pastures.
I think one of the big take-aways in these situations for many people is the realization that just because a person is trans does not mean that you will by default have anything else in common or get along with them any better than you would a cisgender person.