Moslems have decided to disagree with Denmark on the point of cartoons, and are boycotting Danish products. Meanwhile, Westerners have decided to disagree with Iran on the point of Israel, and are planning Iran's global economic isolation.
I don't actually agree with this, but I'm trying to come up with a comparison...
Also, the boycotts of Danish products in the Middle East are to a large extent government-driven: the Saudi gov't has removed the wares from supermarkets and the Egyptian Parliament unilaterally voted to encourage the boycott, etc. In the latter case, the EU is threatening to bring the matter before the WTO.
However, consumer boycotts as such are of course legitimate. In my lingo above, they may or may not be commendable - cf. this debate - but they are permissible. The world's northernmost desert wind.