I don't believe that's accurate. I've heard first hand from lawyers that the bill of rights guarantees protections from government action, not other citizens or entities like corporations. That's why, for example, we have to have laws that make it illegal for people to break into your home and steal stuff. Otherwise, we could just apply the 4th amendment.

No individual or company has to necessarily "respect" your first amendment right to free speech, as that is something that can only be violated by the government or a government affiliated entity for which these protections also apply.