Those who use violence to put their point of view are, by definition, terrorists, and the leaders of our our civilisation have rightly said they will not acquiece to terrorism. Whether the differences are over anti-authoritarian votes, secularism, beauty contests, or the right to make political comments that may offend, violence is unacceptable, and must never be kowtowed to. Otherwise we accept that might makes right, and live our lives in fear of the bullies and mobs.
The cartoonist's vision is as God-given as Mohammed's, however we mortals may wish to exult one of God's children over another. None of us has the right to decide what God's opinion is of others.
One of my earlier adult works was "The Continuing Adventures of God", and while I was fairly agnostic at the time, I had confidence that if there was a sentient intelligence creating this world, it would obviously have a very good sense of humour. Now that I am more confident that my reality is not simply random and unconnected, I am more convinced that we have not only a right but a duty to express ourselves, whether others choose to be outraged by our opinion or even offer us violence for it. In the parable of the talents, the one who hid his talents out of fear had them taken away, and the one who risked most gained even more that his own profit.
Jesus, after all, carried on with his sabbath healing and such despite the anger of the Pharisees, and he demonstrated that you can only have abundant life if you are true to your conscience regardless of the consequences (whether that be embassy bombings or crucifixion).
I think I might dust off those old cartoons....