Liberty and equality have been the core of American Idealism since its inception. Though they conflict at times, on the issue of gay civil rights, they do not. Gays have the right to be treated in the exact same fashion as straights (equality). And our emphasis on individual liberty demand that the individual be free to do as he pleases so long as his actions do not have adverse consequences.
There is no justification for the persecution of gay people that can even remotely be called "American." The US was partially founded by people seeking to escape from persecution because of their lifestyle (aka the "Puritans"). And now we've come full circle, with the religious seeking to persecute those not like them, unfortunately there is no longer a land for the persecuted to flee to.
Religious reasons used against homosexuals are irrelevant, check out the separation of church and state essay if you think otherwise. Besides religion is a lifestyle choice, being gay is a biological/psychological character trait - when the two come in conflict, those who have a choice in the matter are the ones who should be pressured to change.
And just because a majority want something doesn't make it right (think Germany 1930s). I know a few people who think that religious people should be lobotomized and committed to mental institutions; but even if a majority of the nation believed this, it wouldn't make it the American thing to do. You may also have the US confused with a democracy...this is a nation of laws with built in safe-guards against tyranny of the majority. Although sometimes, as the US Congress has recently demonstrated, these barriers against legislation of fear and hate break down.
Yes, the government has a duty to protect the institution of family, but what does that have to do with anything? Can anyone tell me how the persecution of gay people is going to protect the "American family" (whatever that is)? If anything it will further split gay people from their straight families - though maybe that is how "family values" is defined by conservatives.
If you think the American Ideal is anything worth fighting for, you will support gay civil rights.