Over at the wonderfully-named Iranian Redneck blog, Darren Sherkat highlights some fascinating data from the General Social Survey. The chart covers public opinion from 1973 through 2012. The blue bar represents people who describe "homosexual sex relations" as "always wrong"; the red bar shows the people who say such relations are "not wrong at all."
The image pretty much speaks for itself. Note that the turning point comes in the early 1990s. The comment thread is open for speculations about why the floodgates would open at that particular time. Bear in mind that politics and pop culture tend to follow trends rather than setting them, though they can reinforce a trend once it's already underway.