Why does it seem that I'm the only one who thinks Trey Parker & Matt Stone were in on this censorship? Mind you, the network claims to have censored not only the dialogue but also the visual depiction of Mohammad. If you watch the episode more than once, you should become very skeptical. So many "censorships" are directly used as jokes. Had they not censored, where would the comedy device exist in those scenes? I'll elaborate...
Tom Cruise's satire immunity
Once Tom Cruise gains Mohammad's power, the view closes in on him and he dramatically becomes censored, a blatant joke. Once he's made fun of for having Seaman on his back, the bar is removed. The black bar concept is clearly used as a comedic device and the events wouldn't make sense without it. Why would a fearful network that's legitimately trying to censor its episode bother messing with Tom Cruise at all? South Park Studios did this just as they censored Mohammad. Hell, Mohammad's body was probably never animated into the episode to begin with. The humor wouldn't exist without this censorship.
Censor bar movement
Even though any character standing still remains entirely static, the censor bar over Mohammad constantly wavers, inevitably drawing the viewer's attention. It also comically hops from side to side as he walks. If this were true censorship with no other purpose, the bar would likely sit still when Mohammad stands still and simply pan smoothly instead of hop around as he walks. In fact, extra work would have been required to make the bar as restless as it is.
When Seaman attacks Tom Cruise, who's simply standing in place amongst chaos, he first declares his attack before jumping on him. He then awkwardly fights the censored Cruise in a comical manner relying totally on the censorship bar.
The "I learned something today" monologue
When you watch this scene, note how Kyle really braces for it as he delivers the famous opening. You anticipate something special will happen and it does when his entire "speech" is censored. But not only does Kyle speak, so do Jesus and Santa. Would that really be necessary to have three characters attribute to the final speech? That's major overkill and it seems very obviously intended for humor as each character's dialogue is blanketed in a long-drawn beep. Why on Earth would they need to rattle on for about 40 seconds of pure humorless dialogue? Surely the studio could have condensed the speech down to its major points. And why does Stan cock his head and give a cute, approving "Yeah" in response to their speech? This comedic nature is entirely dependent on the censorship.
If dialogue truly was censored, surely in time the studio should be free to at least release a transcript of the Kyle/Jesus/Santa monologues. And we should be able to see how well their mouth movements match it.
If my notion is correct, SP Studios did this to stir up controversy as we know they love doing. They were able to both censor and appear courageous with virtually no consequences. Instead, the network gladly took the heat, in exchange for publicity and ratings for one of their top programs, while SP Studios came out smelling like a rose.