“Illegal” is going to depend on the jurisdiction. For example, in the United States, the Online Copyright Infringement Liability Limitation Act provides safe harbor for service providers (such as someone running a Discourse site) against actions of their users. As long as the service provider responds to notice of infringing activity, and can produce good records of what that user did or did not do (emphasis hint for @codinghorror), and how they responded to that user and that user’s infringing content, then they are generally not liable for those actions.
In other words, it may not (or may, depending on where you are) be the job of the service provider to police and snoop on its users’ activities.