> For example, a Republican in the US will perceive "liberal bias" in any story that doesn't present Republican politicians in a positive light, regardless of its veracity.

I think this is a bit of an exaggeration.

There are some Republicans who continue to criticize trump freely, after he won the nomination, even if some of these might still prefer him to Hillary Clinton.

Though some republicans would probably interpret almost any criticism as bias.

Did you mean most republicans or just at least some?

Maybe you meant things that criticize republican politicians as a group? To me, that seems likely to be more true.