There are many things that can happen at a protest that could go wrong. The protesters could be disturbing the peace, blocking a fire exit, or be on private property. But the biggest one is violence. Once a protest gets out of hand and becomes a riot, innocent people could get hurt. Once violence is displayed, people begin to take the problem seriously in two ways; the first being the safety of others and the other being that the protesters means business.
In the play Julius Caesar, the Conspirators ganged up on Caesar and killed him for the good of Rome. If you were to put that into modern terms, that would be like killing the President of the United States for being a bad president. In most, if not all peoples eyes, that is the very worst thing that should happen to someone. Most problems can be solved in a non-violent way, such as kicking the president, or for the play's sake, Caesar out of office.
In some very rare cases, violence is needed in stripping someone of their power. For example, there was absolutely no way anyone could stop Osama Bin Laden unless he was physically taken down. But in the play, Antony had pointed out that Caesar had declined the crown three different times, and that he was not power hungry like today's dictators. So there really wasn’t an explainable reason why the Conspirators murdered Caesar, except that they thought it was the right thing to do.