This seems like a textbook example of the advantages of the separation of religious law and general law. Muslims should not depict Mohammed in cartoons but non-Muslims are not so constrained, except to the extent that doing so will lose the non-Muslim's business. As Albion's Seedlings notes, however, Saudi Arabia has limited leverage over Denmark since Danish exports are largely ham, lager, and bacon. (One of the comments does note that a Saudi boycott of Danish products will reduce Saudi utility by depriving them of Bang & Olufsen speakers. That would be a major loss.)
It also points out the importance of distinguishing clearly the role of the state from the role of the private sector. The Danish prime minister seems absolutely correct in refusing to make any apology for the Danish newspaper, noting that he has no authority over Danish newspapers. Politicians are all too often called upon to speak for their "nation". A little more humility in national capitals and a little less speaking on citizens' behalf would be a good thing, I think.