As Elnoa said, they kind of already ARE accepted/considered part of the community.
And gender and sexual orientation don't have to do with one another, but they do, which is precisely why being gay, lesbian or bisexual "matters."
The same questions come up for people who are attracted to the same sex. Especially the ones who possess qualities typically associated with the opposite sex, be it a particularly masculine woman or femme guy, whether they *wish* they were of the opposite sex. Does a woman wear a strap on because she wants to be a man? Well, no, not usually, but you can see where people unfamiliar can get confused.
Trans people are basically the opposite, except not really, as you can be a straight, gay, les, or bi trans person.
Which is where the "queer" comes in, welcoming basically anyone with quirky shit going on identity one way or another.