How? They have been allowed to be part of society. But society has obviously certain rules. For example, if you murder people, you go to jail (at least usually). Person can be part of society, but it doesn't necessary mean person can do whatever he wants.
Homosexuality is not a case of what you want to do. It's a case of who you are, just like being a woman is a case of who you are, or being black is a case of who you are, or being Native American is a case of who you are. Society does not treat blacks, women, or gays as equals. It's not because those groups are not choosing to fit in to society, by not being blacks, females, or gays.
They want Native Americans to give up being Native too, and act like Christians instead. This is
exactly the argument you are making for gays giving up being gays.
Society is the one in the wrong for not accepting people in who they are naturally, trying to make them give up their "otherness", their Blackness, their Native'ness, their gayness, and so forth. In other words, the true sinner is society, not the gays, or the blacks, or the females. In other words, the log is in your eye, not theirs.
I would try to conform to the standards of Christian love and acceptance instead, as expressed in the biblical texts, rather than conforming to the standards of White conservative Protestant traditionalist norms that calls being non-inclusive of others as what Christianity is. Christian love is suppose to be a
radical love, going against the "righteousness of men", or social expectations of others to their harm, as is the case here.
Christian love is supposed to break down these walls of us and them, not build them higher like this. "They're welcome to be part of us, if they give up being who they are and become one of us instead". "We'll welcome Native Americans into society, if they become like European Christians like us. We'll even put them in schools to take away their old, sinful ways. Then they'll be pure and good and righteous like us. One of us."
This is exactly what you are saying about how gays are welcome in society, if they quit being gays. That's not what Christian love is. That is the systems of the world. That is the "ways of the world". That's not what Jesus taught. Jesus taught something radical. Loving other and accepting them as others to ourselves.
That's a much harder commandment to follow, than trying to "convert them" to look like us. "If you love those who love you, what reward will you get"? If you only love those who are exactly like you, is that really love?