A lot really comes to the overall attitudes of people in the group. Obviously it will stick up for the majority group within its interest group, but are they generally supportive of others whose needs diverge a bit from the "run-of-the-mill" or highly-visible members (and do they listen)? A GLBT group might ignore the T, a Trans group might accept TS or CD but not Androgyne, and any group might disregard how gender, race, religion, culture, or economic class may intersect with any TG subgroup. These types of problems can infect about any group, so maybe what is just as important (if not more important) than the group's purpose is the group's culture. How does it respond to difference?
For me, I've had success attending a UU church (it was sort of easy for me to adopt a more mixed style of dress, because I wasn't going to stay unless I could be accepted there in accordance to its stated philosophy), but not all UU churches are the same, and people can have different experiences depending on their needs and expectations (as also depending on which individuals they talk to). I've also had some success with family and friends depending on the person, even when they do not identify with groups with a history of acceptance.
Groups that are more progressive tend to have better success rates, but the only way you can be sure about whether a group is able to respect your needs is to check it out. If it doesn't respond well to you, try another one. Keep at it.