I assume you're referring to copyright laws and safe-harbor provisions.

But aren't copyright laws another way of suppressing free expression? It seems contradictory to say that it's not ok for Cloudflare to suppress the free expression of Nazis while implicitly supporting the suppression of the expression of file sharers, remixers, and other violators of copyright who want to use Cloudflare. Furthermore, you seem to be arguing that the explicitly political expression of Cloudflare's CEO should be suppressed using the power of the state (by suggesting that it should open them up to legal liability).

I wasn't referring to copyright laws. If someone in the "move bits from point A to point B" business wants to make it their responsibility to suppress activities that are legal, purely on ideological grounds, then they should also shoulder some responsibility for the activities they're facilitating that actually are illegal and actively harmful. I mean, priorities! Otherwise they should stick to moving bits from point A to point B, cooperating with lawful orders when required.

You mean beyond taking it down after it's reported? Surely they already do that.

Are you suggesting that in order for them to be allowed to turn down Stormfront's business they must take on the legal obligation of actively screening all their content for illegal material?

I don't see the connection or justification.