Whether a person is gay or transgender through genetics, choice, environment, or any other reason does not matter. They are the way they are, and they have just as much a right to be who and what they are as the rest of us.
I think that view is extremely naive. Because our society is constructed such that it imparts harm to and discriminates against the gay and transgendered, it does indeed matter whether or not being gay or transgendered is a choice.
Yes, they do have the rights you describe, but those rights are not recognized. If being gay were actually a choice, it would be quite a foolish choice to make here in North Carolina, where in all likelihood the right to marry or even to form a recognized civil union is going to be put forever beyond reach next election.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison