Are we talking about the scene where they discover white privilege?
I think that scene perfectly encapsulates what the poster is talking about. Beavis and Butthead are morons. We laugh at them because they are beyond stupid, they don't understand things in the most comic way possible. So they learn of the concept of white privilege and they take it at face value. They accept the premise and they go on their little rampage because that's what they think it allows them to do. Even though they are wrong. They are a caricature of the entire concept. And everyone can laugh at it.
The left because, to them, it's 'lifting the veil' so to speak. They are taking white privilege to the extreme conclusion. While no one outright acts like that, they feel there's the element of truth to it. The right because, like I said, no one outright acts like that. When Beavis and Butthead get their comeuppance, they can say, "See, even though they are white males, they still can't do whatever they want. There are rules."
Have you seen the new Beavis and Butt-Head movie, it was very much more explicit in making lazy political jokes, albeit mostly for one filler scene.