I don't believe they can. But they are also a common carrier, unlike ISPs and similar. Once ISPs become defined as common carriers, then the argument will have more merit. But expect that to happen anytime soon, because the big guys like Comcast and Cox don't want to allow anyone and everyone to have access to their infrastructure.
All I'm trying to highlight here is that our government already does have some limits on what infrastructure companies can do to shut off service to customers. I feel that Internet infrastructure companies like Cloudflare should have at least as much responsibility to be content neutral as a phone company, and I do hope the law catches up here.
I certainly don't think it would be "unconstitutional" to bar infrastructure companies from moderating content, like we already do with telcos.