The concept of free speech does include the right to be heard in that if I want to hear what you're saying, the government preventing me from hearing it is just as bad as preventing you from saying it. It takes two to communicate.
However if I don't want to hear what you say--or I don't want to help you say it--the government is not going to step in and force me to do it.
The distinction is really about depriving vs. providing.
People get it mixed up in their heads when it comes to contractual relationships like Cloudflare. On one hand it is grammatically correct to say that Cloudflare is "depriving" 8chan of their service, since 8chan used to have access to it. Legally, though, 8chan never had any right to Cloudflare's service. It was a privilege that was revoked.