I'm not T, just an SO in a heterosexual relationship. Also not L or G, but maybe B. So feel free to ignore this.
The reason homosexuality is persecuted has little to do with the fact that some people like the same sex (don't yell at me yet!). It has everything to do with the fact that liking the same sex (or, worse, actually *having* sex with the same sex) is a violation of the expectations others have on a person based upon the socially acceptable gender roles for someone of the person's perceived gender.
Basically, a gay man is wrong in the bigot's eyes because he's not acting like a man. The transgender woman is wrong for the same reason - she's not acting like a man (the bigot sees her as a man). But in both cases, gender stereotypes are being enforced upon the victim by a third party, and these stereotypes are just not based in truth. In one case, the stereotype about what partners are acceptable for a man is a bogus stereotype about men. In the other, the premise is wrong - she's female, not male. But a huge chunk of the problem is that the stereotypes are enforced, not just that the wrong one is applied.
There are differences in the subgroups that make up LGBT*. L's have different issues than G's (for instance, they have the double minority status of being women *and* lesbian), which makes things different. B's are different than L's or G's, because they don't really fit nice neat categories. "I don't know who I might be attracted to tomorrow' isn't easy for people to understand. And obviously T's have issues that others don't (although there are many different subgroups of T's that have different issues from each other - I'd say an MTF vs. FTM's experiences differ in significant ways, that people who want to live between-genders/without-gender/both-gender/other-gender are often not having the same experiences as other T's, cross-dressers have different issues and concerns than other T's, etc. Even within the T community, I can see even as an outsider that not everyone who identifies as part of "T" considers everyone else who identifies as part of "T" to be a legitimate member. But somehow it's only okay for T's to ally themselves with a group that is more cohesive than T is itself?
Now there are also differences. There are issues which are just G issues, or just L issues, or just B issues, or just T issues. But there are also issues that affect everyone who has violated someone else's idea of what gender roles are acceptable. And then there are issues that transcend LGBT people and include other groups. None of this is a bad thing.
If an entire group all agreed and respected everyone else in that group, I'd probably call it a cult.
I'd say join a group and support them when they are doing the right things. Go your own way when they are not. You might go back and forth with the same group, supporting some of what they do one day, while fighting against it the next. Nothing wrong with that. It's how you know you aren't in a cult.