I understand that people on the right believe that to be true.

But, in fact, things like anthropogenic climate change that the right refused to acknowledge, and believed that the media was lying to them about, are true.

It matters what is actually true. The fact that the two sides may have felt the same isn't relevant. The truth is that it wasn't the same.

Another factor: Republicans think it's authoritarianism when the mainstream media doesn't tell them the things they prefer to believe. But here's another clue for them: It's only authoritarianism when the government uses its monopoly on power to force the media to say what they say. It's not authoritarianism when the media says something because they think it's true, or even when they say it because they are trying to please an audience that mostly thinks it's true.