The Muslims were being parodied as a violent religion, so what do they do to counter that? They perform acts of mindless violence.
The small minority of Muslims performing these acts are not worried about being portrayed as violent: what they're objecting to is perceived blasphemy.
The vast majority of Muslims just want to live their lives peacefully like the rest of us without worrying about cartoons.
Cultural and religious differences aside, human nature is the same the world over. In any group, you have a small fanatical extremist group who wants victory at all costs, and sees good only in their own group, and evil exclusively in others. Some of these, like our own Infidel, are just mindless morons whose creator sadly made them without the critical faculty for deductive reasoning. Some are smart manipulators who see that in a polarized situation, they can rise to power over their own group.
The rest of us pretty much just want to be left in peace. When the group is attacked from the outside by another big group, be it a real attack or a phony one dreamt up by extremists, ours or theirs (911, this cartoon), then this majority groups fragments. At least half respond in knee jerk fashion, willing to believe the extremist's demonization of the other group. They're not dumb, but they're not smart enough or cool enough in a perceived crisis to think clearly, so they rally in unquestioningly behind their "leaders". That leaves the rest of us as the cowed minority, hoping that sanity will be restored.
You can be sure that the ragheads jumping up and down mindlessly attacking Danish targets are the Pablito- and Strawman-equivalents on the other side, not the Monkeyboys and Daras.
He'll have you wrestling midgets in border towns for ten percent of the net.