Or you could just fantasize about finding a billion dollars on the ground. After all, it could happen, so there's an epsilon chance of it happening without doing anything.

You could just say, "Okay, I won't draw Muhammed anymore. It was my mistake, but you didn't need to be so outraged; you only needed to ask and I would have agreed." In other words, you're politely rejecting that you're a bad person because you violated the norm (that wasn't really a norm), but still avoiding a fight.