Because we have police.
That is, not because the police are there to arrest rioters, but rather because we believe that we don't need to rely on our reputations to protect us. At least, this is the "honor culture" theory. There are "cultures of honor" and "cultures of law." We live in the latter. Most of the countries in which there is rioting are the former.
An honor culture comes about when poor people risk losing what they have. Actually physically defending it is expensive. If you get into a fight, you will suffer as much damage as the person you are fighting. The goal, therefore, is to be seen as willing to fight, in order to avoid actually having to fight. It is important that people know that you're willing to fight, because that gives them an incentive to go pick on somebody else.
You can see how it applies to this case. They feel that they've been insulted. An anti-religious message is seen as our declaration that we do not fear or respect them. It doesn't matter that this isn't an actual attack on them; it is a signal that we believe ourselves capable of attacking them. And so they send us a signal in return: they take violent action against nothing in particular, and kill people at soft targets to let us know that they are willing to kill us.
And remember, we've just recently shown ourselves to be willing to go in and disrupt their cultures if we thought it suited us. Their fear is not entirely unwarranted.
Their reaction, however, is. It seems pathetic to us from here. If we wanted them dead, they'd be dead. They're not even close to having the power to stop us. This is a chihuahua barking at a wolverine. A twenty-foot tall wolverine. With machine guns.
Still, they have to send the signal. If nothing else, they have to send it to each other. If you are too weak to try to defend your honor from the Americans, maybe you're too weak to defend it from me, too, and I shall go steal your stuff. They're putting on this show at least as much for each other as they are to us.
Which is all very quaint, except that it comes to murdering Americans, which is a disaster. The chihuahua can bark at the wolverine all it likes, as long as the wolverine doesn't care. Actually bite it, and you find that it gets honey badger on you. The US is trying to show restraint, since it knows perfectly well that retaliation will generate more retaliation. Unfortunately, lack of retaliation can also be seen as weakness, which can be just as bad. The US is forced to rely on the fact that it is so much stronger that it can afford to ignore this, along with the use of back channels to try to stem the disaster before it gets out of hand.
When riots do happen in the US, they tend to happen when honor cultures within the US feel at risk. The King riots were a prime example. These were poor people who already felt that the police were in a position to do them harm, with impunity. The verdict affirmed it. The verdict itself wasn't a violent act, but it was seen as a threat: you do not live in a culture of law, and the law will not protect you. Given that there was no law, they fell back on honor, which meant a display of force. The force could not, for the most part, be aimed at their enemies. It ended up being mostly taken out on each other. It was a very sad and horrifying day in America.
Christians in America can put on a display of being affronted every year come Christmas, but they still live in a culture of law rather than of honor. A show of violence would do no good and much harm. They have more to lose, economically speaking. So, one would not anticipate Christian riots when insulted.
The theory of "culture of honor" and "culture of law" originates from the book
Culture Of Honor: The Psychology Of Violence In The South by Richard Nisbett and Dov Cohen. It's still in print:International Politics: