My favorite stupid protest locally was when a large mob of people decided to protest against cars, so they clogged a bunch of streets. Since they weren't cleared to do so, the cops arrested a lot of them. Then, the protesters tried to paint the cops like Nazis, even though what the protesters had done was blatantly illegal.
My favorite all time stupid protest happened at my Dad's office. He once worked for a really small, like less than 10 people, oil company. One morning, the entire front side of the building was picketed by a sizable group. In fact, there were many times more people protesting than there were in the company. And what were these geniuses protesting? The big bad oil company that was drilling in some environmental place that the protesters wanted to protect. Of course, nevermind the fact that Dad's oil company was not then, nor was even planning, to drill any wells within a hundred miles of that place, but hey, don't let a little thing called "reality" get in the way of a really good protest. I mean, you might score at one.