The relevance of the Holocaust to the Danes is hard for me to see.

They seem not to be attempting to aim this response directly at Denmark.  But rather at the West and its values in general - based on a perception that thh West is hypocritical in that it would claim "free speech" in defence of the Mohammed cartoons but not so in defence of cartoons ridiculing the Holocaust. 

This point seems to me to be based on a fundamental misunderstanding of the "free speech" argument.  I expect many people will find holocaust cartoons appallingly offensive, and are likely to be vocal on that point.  I expect the prevalent view will be that it is grossly tasteless to run this competition (particularly since as you observe there is no direct relation between Denmark and the Holocaust) but that papers have the right to publish what they will.

Perhaps there will be some debate over whether holocaust cartoons amount to incitement of religious hatred - it may come down to the individual cartoon itself.

I'm afraid the nuances in the distinction between having the right to do something, and being right to do so it will elude the inflamed masses and I expect this contest will seem like a slam-dunk riposte to some.  It appears on this issue  we may have moved beyond the possibility of constructive conversation.