I agree that there is a difference between the two of them and I think in both cases if any termination is going to happen, it ought to come from the legal system itself as a Court Order.
A piracy service causes no immediate harm and should be dealt with legally, but something that has been proven to cause harm (actual harm, not feelings or whatever the minorities keep crowing about) should be preemptively terminated and should not require a court order - in this case terminating them does not infringe on any incorrectly assumed rights as they aren't being censored they're still free to participate on the internet.
More importantly, it's not a legal decision it's the moral and humane choice.
something that has been proven to cause harm ... should be preemptively terminated and should not require a court order
I don't see why. Law enforcement has been dealing with exigent circumstances since before the Internet existed. It's a problem that they refuse to do their jobs in many cases, but we should fix that rather than privatize it.
Yes absolutely, I agree entirely law enforcement should do their job properly, but that doesn't absolve everyone else of a moral responsibility. If they were maiming children or kittens nobody would argue for a court order which could take years, they'd demand it be removed (which happens voluntarily in many cases, like child porn).
The point is there needs to be discretion here, it's not black and white which is the stance cloudflare are taking and burying their head in the sand while it continues.
Fyi cloudflare still hosts a bunch of sites which deliver both.
More importantly, it's not a legal decision it's the moral and humane choice.