Comedy Central did face substantial criticism.This in my view is the first actual decent point in defense of the idea, or the principle of participating in such a day.
Thing is though, the reason something was censored in the show, which does this generally as a form of art (contain offensive things) was not Muslim's fault. It was the decision of the people responsible for the show, as a result of some threats by a few individuals. They've already shown Muhammad before. So its not a question of Muslims getting special treatment, but rather as you pointed out, the idea of giving in to such threats that is the real problem, and the thing that is worth criticizing.
Thats not to say that Muslims don't have special 'needs' in this regard, and that as a result Muhammad might be generally depicted much less, if at all. But to say that the real problem is the idea of threats of violence actually working in forcing or pressuring the show to reconsider.
As such, while offending people generally, or doing something that others don't like isn't necessarily bad, responding with something that does step over that special 'need' of Muslims, while knowing that it would also include such an amount of hateful messages (although that is not the goal) by bigots who inescapably take advantage of the day to have some fun, might not be a good idea. Unlike the show which does this generally as a form of general expression, not an emotion filled response to some individuals or some incidents.
Put differently, as i've said in other posts, considering the amount of unnecessary damage done, other methods would've have been the wiser choice. Knowingly choosing to do this despite knowing that you'll hurt a lot of Muslims needlessly, while also knowing that they had nothing to do with the incident you want to object to, is ill-advised in my view.
I wouldn't specifically say the censorship was the result of some threats by a few individuals. That event didn't occur in a vacuum. Between the earlier episode that allowed Muhammad, and the later episodes where he was censored, in addition to those specific threats against Comedy Central and South Park, there were several major instances such as Theo van Gogh being assassinated by a Muslim for producing a documentary criticizing the treatment of women in Islam, and the controversy regarding Danish cartoons depicting Muhammad, which resulted in a wave of protests in multiple Muslim-majority countries, reported deaths, and violence at Danish embassies in more than one country.
So with regards to anything related to Muhammad (but not Jesus, Buddha, Krishna, secular concepts, etc), Comedy Central has to make a rather philosophical decision. Do they arbitrarily censor content that is equally offensive, or even less offensive, than other content that they show, simply because it could have an unusually negative reaction? If they allow content that, indirectly, results in deaths somehow or some place, are they partially to blame? If they know that releasing the content has a chance of damaging them financially, are they responsible if they let it come out? Now, for a show that is often potentially offensive in any given episode, they may face these challenges from time to time, but apparently some subsets are more difficult to criticize than others.
Looks to me like Comedy Central was stuck between a rock and a hard place. The rock was the concept of free speech and consistency/favoritism of censorship. The hard place was the subset of Muslims that would cause or attempt to cause violence in response to a cartoon show that they didn't like.
So Comedy Central folded, and faced criticism for it. But what of the mass protesters and embassy-attackers in multiple countries that apparently support violent behavior in response to non-violent cartoons? Is it worthwhile to say to them, that what they do will not work?
Especially over the last 20 years, the world has become increasingly interconnected in terms of information due to the internet. A media group in one country can be seen by people in other countries. Cultures and their values can clash.
In your post, you granted that Muslims have special needs. I'd propose a refinement that, a subset of Muslims apparently have special needs. Out of the 1.5+ billion Muslims in the world, even if 15 million of them protest or cause violence, that's 1%. If 1.5 million protest or cause violence, that's 0.1%. If 150,000 protest or cause violence, that's 0.01%. There certainly weren't 1.5 billion Muslims causing issues in response to cartoons. The issue, of course, is that even a rather small number of people (whether it's small meaning a few individuals, or small meaning thousands of people out of a much larger group), can cause damage.
It doesn't seem to me that media groups or individuals should be censored in an imbalanced manner due to a fairly small subset of a group. If Comedy Central doesn't face financial or life risk by heavily criticizing Jesus, heavily criticizing Buddhism, heavily criticizing atheists, heavily criticizing liberals, but does face financial or life risk by heavily or even moderately criticizing Islam, then this is a problem, and a question.
-What is it about Islam that this becomes a problem? Is it a coincidence, or due to the religion, or due to the surrounding cultures in numerous countries? (Instances such as the specific Comedy Central threat, which was from a caucasian American-born Muslim convert can shed some light on those questions, albeit with only small sample sizes.)
-Regardless of what the causes are, if identified, can they be addressed and minimized?
-In an increasingly interconnected world, should everyone tiptoe around Islam due to the subset of individuals that don't believe in the same freedoms of expression, or is it better to never cave into it, and desensitize the issue until it's not an issue anymore? Should Islam receive special treatment, or should it be treated in the same fashion as any other religion, any political idea, any cultural element?
This event was aimed primarily at the subset of people that are not okay with freedom of expression. Not the 1.5 billion or so Muslims in the world.
-If South Park makes fun of atheists or liberals, which they have, I'll either find it to be silly or funny, but never offensive. They're not violently threatening me. They're not necessarily even insulting me personally, or implying any insults. If South Park gets censored, and a wave of people make fun of some concept I consider important, to what degree should I be offended?
-Similarly, if I see "death to America" signs in foreign protests, then frankly, it doesn't affect my emotional state one bit. They're frustrated, they might not hate me if they met me in person, and even if they still do, that's ok I guess as long as I am not in acute danger from them. But the point is, I'm not going to internalize and be offended by every criticism, every offense, that could relate to me in some way. Draw Muhammad Day need not be any more offensive to anyone, than any other silly, nonsensical, satirical, offensive, little stunt. Various sorts of media and individuals can and do criticize or make fun of various ideas.