Im a muslims myself.
I dont think drawing Muhammed is offensive at all. He was a man just like all the other prophets. If you take offense in him being drawn or ridiculed, then you must also take offense at Jesus being drawn and ridiculed.
My only problem are the references that incite hatred, like the bomb on his head, he's paedophile, or depicted as violent, which suggest this is what Islam is about. Which is rubbish. The people who are behind this are complete islamaphobes. Which is the real reason why muslim should be up in arms. Its the faith you should be defending not the man.
Throughout the ages, there have been depictions of Muhammed looked like, but this was frowned upon in Muslims, but no one recieved death threats, only because of reason we should not worship Muhammed, that is shirk, one of the biggest sins of Islam.
But even today, Muslims have given such incredible adoration for Muhammed, that even a drawing an image of him is blasphemy, Im sorry but that is 'borderline' adering Muhammed as a god., which is completely forbidden. You cannot put Muhammed on the same status of God, to do so is shirk (Islam biggest sin)
Ironic isnt it? (well atleast the athiests will find it ironic)
Conclusion: South Park (anyone) have the right to draw Muhammed, in a way that doesnt incite hatred for Muslims or Islam
This is why ladies and non ladies, peace will never come to humanity, we will destroy our selves, its a vicious cycle.