Whether the satirical Twitter account should be shut down or not ... satire's not very effective per Malcolm Gladwell's "Revisionist History" podcast at [0] (automated lossy transcript at [1]) ... targets of the satire often find the satire humorous themselves, and can find enough "truth" in exaggerated viewpoints to reinforce those views rather than call them into question.
Whether or not speech is effective at achieving its ultimate goal is an entirely irrelevant issue here. "Hate Speech" is extremely ineffective at promoting hate, but here we are.
I personally wouldn't trust anything that Malcolm Gladwell says on the face of it. He has through out his books used anecdotes as proof, and often cites correlation as causation. He spins a great yarn, but that's all it is.
[0] http://revisionisthistory.com/episodes/10-the-satire-paradox [1] https://blog.simonsays.ai/satire-paradox-with-malcolm-gladwe...