It is generally the left that promotes turning away from anything offensive. Unless of course, it is a Nativity, or something else, that they find offensive. The right generally tends more toward trying to have standards of decency. A very tough battle in America today.
As for the merits of the "just turn it off" argument, it's questionable whether that is a good standard when you have only adults watching. But if we think there are things that kids shouldn't see, "just turn it off" isn't going to cut it. We are told to supervise our children if we don't like what's on the air or on the Internet. Yes of course, we should all supervise our kids, and we certainly do when ours is at home. But I cannot supervise her every move, such as when she visits friends, etc. If it is on TV, or on the Internet, kids are going to be able to see it no matter how careful their own parents are. And you know that even the friends that seem the nicest are capable of looking at almost anything. So just turning it off at home, while that is good and somewhat effective in that it communicates your standards to your child, isn't a solution.
Bottom line is, I should not have to have a friendless hermit child in order to protect her from the worst garbage.