It's less true than it used to be, but there are still some people who take exception to that. (And when I say "take exception to that," I mean write great honking essays about how "AMERICA'S LOSING THE CULTURE WAR" and how Murphy Brown caused 9/11 and crap like that.)
Unmarried heteros sleeping around is pretty much matter-of-fact these days to the average person... unless it's their daughter doing it, of course, and then someone has to die.

Unmarried heteros _breeding_ and remaining unmarried also has less of a stigma than it used to, though the approval rate isn't as high on that one.