No business is completely a dumb pipe, the DMCA provisions are very specific and are increasingly overruled once enough (copyrighted) content is in place.
Cloudflare also specifically removed that site for a stated reason that they claimed CF was helping them. That is outside the bounds of the site content itself and is a perfectly fine argument to stop doing business based on libel and misrepresentation.
Cloudflare also specifically removed that site for a stated reason that they claimed CF was helping them. That is outside the bounds of the site content itself and is a perfectly fine argument to stop doing business based on libel and misrepresentation.