Depends what offends you. In this case I think the people saying "move on" are mostly telling homophobes to leave people alone. And I'm completely with them on that.
I'm not offended by people loving each other. I AM offended by people selling the secrets of the ancient Nazi alien Templar conspiracy code, with Bigfoot. And I CANNOT come to bed right now, because someone is WRONG on the Internet! The story of the Holy Grail was invented in the 12th century by Chretien de Troyes -- I'm not mad at Chretien, he never pretended that he was writing nonfiction -- and I CANNOT rest while the History Channel makes hillbillies believe that they can dig up the Grail in the woods right next to their homes! Chretien made up the Grail! In the 12th century! That's when it was made up! And by whom! And I will not be silenced!