A little recent history:
A newspaper in Denmark published some cartoons of Mohammed. There were riots all over the world.
Most of the Western press did stories on this, but did not show the cartoons themselves, supposedly so as not to offend muslims. A few did but faced consequnces - Borders refused to carry a magazine which did; a few college papers did and their staff was suspended.
But only 2 of the 15 cartoons were even critical of Islam, most were harmless and a couple were critical of the paper that ran them. Which is why it was important to show the cartoons in order to understand the story fully.
Most western governments condemned the cartoons. Despite most of them having "Free Speech" in their constitution (or whatever they have in Europe). The US government had sort of a mixed message, disappointing many free speech advocates. The UK foreign guy, Jack Straw, vigorously denounced them.
At the same time, South Park ran into trouble with two recent episodes getting pulled from re-runs. One about Scientology, and one which had a small gag about Catholics (a Virgin Mary statue having a period).
This is their response to both issues. They just happened to use Family Guy because well, there's only 1 other popular animated show besides them (The Simpsons), and they've already used that. Sure, they might be critical of their jokes (for reasons depicted in this episode. Which is true, but that is part of Family Guy's charm), but that wasn't really the point.
Some people get it, but most do not. Or have their head in the sand.