"free speech" only makes sense in the context of government regulation (vs individuals/corporations), because governments have a monopoly on violence. As soon as two non-government entities are "regulating each other", it is a matter of mutual free speech. e.g. what about the free speech of Spotify?
Rogan sold his intellectual property, i.e. his speech, including the speech of his guests, to Spotify. Now depending on the contract (I do not know what the exclusivity clauses look like) Rogan might be able to host that content on other platforms, or he might not. Either way, on Spotify's platform, legally the speech is Spotify's not Rogan's nor the guests.
FWIW, if recorded conversations/speech cannot be considered intellectual property, that can be bought and sold, all current media will be impacted as it cannot be run as a business.
The line is when you take actions designed to prevent someone else from ever speaking, or people hearing their speech, instead of (as is your right) loudly calling them a *ist.