Scott Adams has been a star for a couple of decades now, so of course he believes be deserves preferential treatment and that normal workplace rules don’t apply to him. Stars have always believed that, and extreme cases like this aside, they’ve always gotten away with it, too.
The flip side about stars, though, is that they are never truly on their own time. So when they lip off in public, the consequences also accrue to the people and organizations they are closely associated with, which in this case is the newspapers in which Adams runs. The Plain Dealer was the only place the folks in Cleveland could see his work. When they think of Dilbert, they think of the Plain Dealer, so when Adams goes off like this, his actions are associated with the Plain Dealer as well. In such a case, they are practically obliged to let Adams go. It’s the same thing if a player lips off in public, even during the offseason—he is associated with the team he’s on, so they’re going to bear the brunt of criticism, too, so they have every right to sanction him within bounds as they see fit. That’s something most of us don’t have to worry about when we ourselves lip off in places like this. Yup, it’s totally not fair.
The last thing here is that Scott Adams also wasn’t really on his own time, anyway. He was trading on the fame he gained through his association with the newspapers to host a live stream in which he could spout off his noxious views in the first place. He wasn’t doing this on his free time—he was still working, making income due to his associated fame, which he couldn’t have done so prominently had he not acquired that fame through the newspapers he was still being featured in. Even if the papers don’t share in the revenue he generates from it, they still bear the brunt of the externalities his bad behavior generates, anyway.
Any newspaper dumping him because of this is totally in the right.