It's not so much that they are offended by the content of the cartoons, it's because its forbidden in Islam to have any depictions of the prophets of the Abrahamic religions and of God. That's why all of Islamic art is abstract or more geometrical and about the text and language...no images of humans-- that dominate much of Christianity and Hinduism.
I think the response to these cartoons is inflated in the west. There is a tradition within Shia Islam of painting all the Shia saints and there are numerous paintings of Muhammad. I have a photo and seen one in Baghdad.
Below is a portrait of Muhammad in my Uncles library in Baghdad.