The U.S. Has a Bill of Rights
Comedy Central reserves plenty of rights in regards to what gets broadcast on their station. That's their prerogative. I can respect that to some degree. The idea behind first amendment rights is that congress (Federal Government) cannot make laws that suspend any expression, congregation, or religion on part of the masses. They're not meant to support or denigrate particular religions. What the private sector does, however, they also leave alone, for the most part (ideally).
Comedy Central fears retribution from Islamic folk because they know the freak shows who use that religion as a stepping stone towards power and dominion over others is far more real than in the peaceniks of all Christian sects, particularly Catholicism (which practically every comedian shown on Comedy Central has thrown barbs at). There is a clear and present danger when handling the sensitive egos of the Islamic faith, but not with other faiths.
South Park, of course, defies this crap, pushing people's buttons specifically because someone has to. It's like Puck from the 19th century, or Mad Magazine, or any number of underground comics that poke barbs at society. They're not poking at the religion... they're poking at the people. Most if not all the problem with any religion, philosophy, or school of thought, is that the adherents will often use it out of context and separate themselves from others who do not share the same exact ideas in common. Just a bunch of little villages who don't like to speak to one another.
But people don't like being taken as fools. Satire is cynical in nature, and some have no respect for such an attitude. Pair that with the primitive inclinations of people who enter a faith in search of answers... and you'll get a bunch of people who do, in fact, grind axes. Comedy Central doesn't want to be on the receiving end of a bunch of people who will, according to stereotype, throw said axes at them.
Sensitivity is for the weak. Comedy Central should not give a damn and not worry about radical Muslims because they don't give a damn about Catholics, Christians, or Jews either. They should not need to self-censor themselves lest they lose one of their actual programming gems that have weathered 200 episodes, a milestone for that network. But since I don't think they'll back down from their oversensitive micromanaging, perhaps South Park will move to some other network willing to accept a crown of thorns unafraid to speak its mind.