Is your theoretical assuming the entire world is anarcho-capitalist, or just a small state? I think that will change the answer. A propaganda campaign from a Multinat funded by stolen tax dollars from people around the world to influence politics in our little Ancap haven is enemy action and should be treated accordingly.

In a more ideal ancap world, you would have big businessmen who pay for news that makes them look good, but their capital would be a little more limited. You likely wouldn't have the massive corporations that exist today with state support. You would expect other businessmen to pay for competing news. You would not have monopolies on broadcasting, or state deals to subsidize the cable companies that distribute news. You would not have the maelstrom of private + public institutions telling people to get the shot, by coercion.

Also in Ancapistan there is no such thing as freedom of speech. Only property rights. You're right about incitement to action.

And yes dictators often rose up out of power vacuums so I'd fully expect even in an anarchy certain wealthy people would amass as much power as possible around their own cult of personality to convince The People that they need to support a New Order that puts those wealthy people in charge. One of the serious issues anarcho-capitalists often gloss over is that most people are not kings, lords, plantation owners, or even homeowners. Most people are plebs, commoners, laborers working for someone else. Commoners will always exist and be easily manipulated into violent action by bad elites who have sway over their livelihoods.