Using words like "Ching-Chong" on a parody show sends the message that slurs like this are all in good fun. But in a world in which racism still exists, these comments are not categorically funny in the same way other satire is.
When something that we like, something that is usually in line with our "progressive" sentiments, reveals that the ethics of race and racism aren't as tidy as we had assumed, that structure begins to crumble. We become defensive.
The Colbert Report has argued that Colbert's character on the show is simply a conservative, bigoted persona who is simply a comedic archetype. But regardless, the actions of this persona do have repercussions -- intentionally, or unintentionally.
Even awareness of the satirical context did not slake the thirst for outrage of those demanding that Comedy Central (who, you may recall, actually tweeted the out-of-context punchline, not Colbert) #CancelColbert.