First, I think liberals really do believe that conservatives are idiots (or evil manipulative types), and tend to characterize them as either cigar-smoking rich fat cats, yokels driving pickups, or televangelists with southern accents preaching fire and brimstone. Our higher education system is predominantly liberal, so our college grads often emerge believing that liberalism=sophistication. Hence, opponents of the liberal agenda are branded as 'idiots'.
Second, the gay rights groups are well funded, well organized and smart. They have made it their goal to win acceptance, but I don't believe it ends there. I think they want to obliterate their opposition. They attempt to discredit or ridicule anyone who opposes their agenda. Having been marginalized themselves for years, they are going on the offensive and trying to turn the tables on those who stand in the way. Even though sentiment on gay marriage is split roughly 50-50, Those who publicly oppose it are routinely attacked in the media, while those in favor are rarely attacked in the same way, but since the media is essentially controlled by liberals (aside from Fox News, radio, and the internet, obviously), what can you expect?