First, nobody including Muslims have a "right" to live a life without being offended, which is something that appears to happen a lot with Muslims. The problem is that offending Muslims often causes rioting and death. The Danish cartoons depicting Mohammed caused roughly 100 deaths.
http://en.wikipedia.org/wiki/Jyllands-Posten_Muhammad_cartoons_controversy
I think that this self-censorship is driven as much by the implicit threat of violent retribution and/or murder as much as offending delicate, or should I say hair-trigger sensitivities. As has been mentioned, all other religions are targets for comedy but Islam.
Parody is a long established form of humour that is a valid way of highlighting the weakness, illogic, ignorance, hypocracy, etc of a person or group. That Islam is immune from criticism in the media either directly or by parody due to the implied threat of rioting or violence is in itself a shame and evidence of the need for open and critical discussion of the Dark Ages mentality of Islamic fundamentalism.