IMHO, it’s impossible to answer this question. American society isn’t homogenous. Gays are acceptable among certain American cultures, but not in others.
Think of other groups that have had to fight for rights – blacks or women, for example. Blacks were thought inferior for a long time, with all kinds of ‘scientific’ and ‘religious’ reasons to justify this theory and atrocities against them (notably slavery). Today, I think most people are accepting of black folks. Yet, there are still people in this country that will openly call blacks by the ‘n’ word, or who secretly fear blacks, or who thinks that blacks are inherently less intelligent. Women, too, can be in this category – though few men will publicly denounce women as inferior, there is still a stereotypical view of women and some people do really think of women as inferior. Heck, you can find examples of both of these sorts of prejudice right here on the SDMB.
I think gays will go through the same thing. Christianity will adapt itself, as it has for many other issues, and anti-gay bigots will eventually be excluded from churches just as white supremacists are. Notice how the Bible verses about submissiveness and women are not as acceptable anymore? It’s not an accident; Christianity survives because it does (admittedly dragging its heels) adapt. We will also start to understand the science of homosexuality and understanding will help reduce fear. More people will realize that conversion therapy is bunk, and that gay folks do not sit up one day and ‘decide’ to be gay. Gay marriage will become legal, gay adoption more common, and gay partnerships increasingly more protected. However, there will likely be a thread of bigotry for a long time, under the surface, even when we finally reach a point where being an anti-gay bigot is no longer accepted in greater society. Gay men in the workplace will have a time in traditionally ‘masculine’ physical roles, just as women do in male-dominated fields. Gay women will have trouble in fields where sensitivity and nurturing are involved, because of stereotypical perceptions. Jobs involving children will be among the last to fully accept gays, as the frantic “think of the children” cries will bring in emotional issues (and, under the surface, fears about pedophelia and homosexuality). Urban, liberal areas will move quicker; conservative rural areas, much slower.
There’s really nothing in particular that gay folks and allies need to do to accomplish these things, except stay vocal and active. Educating the young is likely the most important part, as it is only through teaching children while they are very young that we will be able to break the cycle of fear and distrust.
Of course, this is assuming that American society as we know it continues in much the same vein as it has. It’s possible we will regress into finding bigotry much more acceptable – in these troubled times, it’s very possible. That’s why vigilance and persistance is important – not just for gay people, but for people of any sexuality.