In a phone conversation in the early afternoon, Mr. Prince sounded torn: On one hand, 8chan was clearly reprehensible, and depriving it of the protection Cloudflare provides would rid him of a troublesome customer and a huge headache. On the other hand, banning 8chan could set a bad precedent, and it could make it harder for law enforcement authorities to monitor violent extremists. Cloudflare, like other tech companies with a window onto dark internet activity, can share information about crimes with investigators.

Banning 8chan “would make our lives a lot easier,” Mr. Prince said, “but it would make the job of law enforcement and controlling hate groups online harder.”

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Among Cloudflare employees, there was disagreement. Some thought that banning 8chan was a clear-cut moral imperative; others thought it could create a slippery slope to censorship. Douglas Kramer, Cloudflare’s general counsel, spent much of Sunday afternoon telling news outlets that Cloudflare would not ban 8chan because of its content, saying, “We’re largely a neutral utility service.”

Hours later, Mr. Prince called me back. He had decided to cut off 8chan. He characterized the site as a “lawless” platform that had willfully ignored warnings about violent extremism. Its tolerance for hate, he said, made 8chan different from other sites where extremists gather, like Facebook or Twitter.

“They’ve been not only actively ignoring complaints they receive, but sometimes weaponizing those complaints against people who are complaining about them,” Mr. Prince said. “That lawlessness feels like a real distinction from the Facebooks of the world.”

Removing 8chan was not a straightforward decision, Mr. Prince said, in part because Cloudflare does not host or promote any of the site’s content. Most people would agree, he said, that a newspaper publisher should be responsible for the stories in the paper. But what about the person who operates the printing press, or the ink supplier? Should that person be responsible, too?