First of all South Park and Family Guy often receive criticism for this kind of stuff.
The real reason, though, is that the targets of these jokes in things like South Park are not black people, gay people, or "tranpires." The real joke is on the people whose ignorance is being examined. It's not literally funny that Borat jokes about throwing jews down wells, it's funny (and sad) because the audience at the rodeo doesn't seem to find anything wrong with it. Randy identifying "I" as the missing letter in "N_GGERS" on Wheel of Fortune instead of "A" isn't funny because it's a funny word to say, it's a punchline about his own willful ignorance.
That isn't to say that these shows/movies aren't beyond criticism, but there's at least something TO them. The transgressiveness alone is not the joke. You keep talking about context, but this bible shit has zero context.