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Republicans and Democrats differ drastically in which news sources they trust and distrust
(www.pewresearch.org)
Source: Pew Research
Democrats: There definitely are some news sources you could at least compare to each other if not trust.
Republicans: Fox news and Joe Rogan all the way folks. Nothing else to see here.
Edit: There is an App called Ground News. It tries to outline which topics get reported by which outlets and where the left and right have their blind spots.
Fox has a 2.67 factor of trust/distrust among Republicans. Rogan has a 3.44 factor for Republicans.
Meanwhile CNN has 4.14 trust/distrust among Democrats and the NYT has a factor of 7 among Democrats. MSNB still comes above a factor of 4 and WAPO is about the same factor like Rogan.
So it is not as much "all the way here" for Republicans. They are relatively more distrusting of all media, including "their" media.
The lower trust in their own media might have something to do with how blatantly dishonest those sources are. But it also likely means that their viewers have lowered any standards they might have ever had. They aren't going to be shocked if they see the lies exposed, they can just shrug and say that everyone lies but the other side lies more.
Obvious falsehoods are dismissed as hyperbole, close enough to the truth that it doesn't matter if it's not entirely accurate. Omissions are just distractions cooked up by the other side to keep us from talking about the real issues. There's no expectation that reporting should be factual and follow journalistic standards, the only measure of the quality of the news source is how much they agree with it. They've been inoculated against reality.