In my view, religion better be a joking matter! Jokes about Buddhism and Christianity and Judaism indicate the currency of these faiths, at least in the US. Few people people joke about Pagan pantheons because they aren’t relevant to the majority. If Islam becomes off-limit for humor, it would happen for only two reasons. One, is that it goes extinct in the minds of the overwhelming majority. That’s unlikely. The other possibility is that its adherents go extinct when enough people decide that it’s no laughing matter but rather something closer to rabies. And I suspect that the exact flavor or sect would be irrelevant to the “killers of the rabid”, same as the nuances of Judaism or Communism were irrelevant to the German troops executing Jews and Commissars.
So the followers of Islam would do better if they developed a sense of humor about their faith the way Christians and Jews have. Those two faiths aren’t judged by the actions of their craziest adherents, and there’s a good possibility that the Western branch of Islam will be able distance itself from the more traditional adherents. After all, my Muslim friends in the US mostly came here to get away from the rule of their nominal coreligionists. They aren’t interested in turning their faith into a government department anymore than Christians here want a Russian-style Synod as a part of the Washington bureaucracy.