There are many legal theories under which Facebook might not be able to kick Alex Jones off their platform. One of them would be the presence of an express or implied contract.

The comment I replied to didn't say anything about the rules of evidence. The Fourth Amendment doesn't, either. It does not prohibit introducing evidence in a legal proceeding that was obtained illegally. It prohibits illegal searches. This is an important distinction. If a police officer illegally kicks down your door and searches your home, finds no evidence of any crime, and leaves without charging you, admissibility of evidence is not in play. But the officer might still be liable under 42 USC 1983 for violating your Fourth Amendment rights. Among others. To say that the law prohibits only cops and not private citizens from kicking down your door and searching your home is dumb, whether they discover evidence of a crime or not, and whether they seek to admit it at trial or not.