Your paragraph on climate change denial among a smart, scientifically educated person reminded me of some very interesting work by a researcher called Dan Kahan.

An abstract from one paper:

Decision scientists have identified various plausible sources of ideological polarization over climate change, gun violence, national security, and like issues that turn on empirical evidence. This paper describes a study of three of them: the predominance of heuristic-driven information processing by members of the public; ideologically motivated reasoning; and the cognitive-style correlates of political conservativism. The study generated both observational and experimental data inconsistent with the hypothesis that political conservatism is distinctively associated with either un- reflective thinking or motivated reasoning. Conservatives did no better or worse than liberals on the Cognitive Reflection Test (Frederick, 2005), an objective measure of information-processing dispositions associated with cognitive biases. In addition, the study found that ideologically motivated reasoning is not a consequence of over-reliance on heuristic or intuitive forms of reasoning generally. On the contrary, subjects who scored highest in cognitive reflection were the most likely to display ideologically motivated cognition. These findings corroborated an alternative hypothesis, which identifies ideologically motivated cognition as a form of information processing that promotes individuals’ interests in forming and maintaining beliefs that signify their loyalty to important affinity groups. The paper discusses the practical significance of these findings, including the need to develop science communication strategies that shield policy-relevant facts from the influences that turn them into divisive symbols of political identity.

Two other relevant papers:

• Cultural Cognition of Scientific Consensus
• Climate‐Science Communication and the Measurement Problem

Parts of your comment reminded me of something that's perhaps unrelated, but seems interesting to bring up, which is Stefan Schubert's prior work on "argument-checking", as discussed on an 80k episode:

Stefan Schubert: I was always interested in “What would it be like if politicians were actually truthful in election debates, and said relevant things?” [...]

So then I started this blog in Swedish on something that I call argument checking. You know, there’s fact checking. But then I went, “Well there’s so many other ways that you can deceive people except outright lying.” So, that was fairly fun, in a way. I had this South African friend at LSE whom I told about this, that I was pointing out fallacies which people made. And she was like “That suits you perfectly. You’re so judge-y.” And unfortunately there’s something to that.

[...]

Robert Wiblin: What kinds of things did you try to do? I remember you had fact checking, this live fact checking on-

Stefan Schubert: Actually that is, we might have called it fact checking at some point. But the name which I wanted to use was argument checking. So that was like in addition to fact checking, we also checked argument.

Robert Wiblin: Did you get many people watching your live argument checking?

Stefan Schubert: Yeah, in Sweden, I got some traction. I guess, I had probably hoped for more people to read about this. But on the plus side, I think that the very top showed at least some interest in it. A smaller interest than what I had thought, but at least you reach the most influential people.

Robert Wiblin: I guess my doubt about this strategy would be, obviously you can fact check politicians, you can argument check them. But how much do people care? How much do voters really care? And even if they were to read this site, how much would it change their mind about anything?

Stefan Schubert: That’s fair. I think one approach which one might take would be to, following up on this experience, the very top people who write opinion pieces for newspapers, they were at least interested, and just double down on that, and try to reach them. I think that something that people think is that, okay, so there are the tabloids, and everyone agrees what they’re saying is generally not that good. But then you go to the the highbrow papers, and then everything there would actually make sense.

So that is what I did. I went for the Swedish equivalent of somewhere between the Guardian and the Telegraph. A decently well-respected paper. And even there, you can point out this glaring fallacies if you dig deeper.

Robert Wiblin: You mean, the journalists are just messing up.

Stefan Schubert: Yeah, or here it was often outside writers, like politicians or civil servants. I think ideally you should get people who are a bit more influential and more well-respected to realize how careful you actually have to be in order to really get to the truth.

Just to take one subject that effective altruists are very interested in, all the writings about AI, where you get people like professors who write the articles which are really very poor on this extremely important subject. It’s just outrageous if you think about it.

Robert Wiblin: Yeah, when I read those articles, I imagine we’re referring to similar things, I’m just astonished. And I don’t know how to react. Because I read it, and I could just see egregious errors, egregious misunderstandings. But then, we’ve got this modesty issue, that we’re bringing up before. These are well-respected people. At least in their fields in kind of adjacent areas. And then, I’m thinking, “Am I the crazy one?” Do they read what I write, and they have the same reaction?

Stefan Schubert: I don’t feel that. So I probably reveal my immodesty.

Of course, you should be modest if people show some signs of reasonableness. And obviously if someone is arguing for a position where your prior that it’s true is very low. But if they’re a reasonable person, and they’re arguing for it well, then you should update. But if they’re arguing in a way which is very emotive – they’re not really addressing the positions that we’re holding – then I don’t think modesty is the right approach.

Robert Wiblin: I guess it does go to show how difficult being modest is when the rubber really hits the road, and you’re just sure about something that someone else you respect just disagrees.

But I agree. There is real red flag when people don’t seem to be actually engaging with the substance of the issues which happens surprisingly often. They’ll write something, which just suggests, “I just don’t like the tone” or “I don’t like this topic” or “This whole thing makes me kind of mad” but they can’t explain why exactly.

I think you raise interesting points. A few thoughts (which are again more like my views rather than "what the research says"):

• I agree that something like the general trustworthiness of the environment also matters. And it seems good to me to both increase the proportion of reliable to unreliable messages one receives and to make people better able to spot unreliable messages and avoid updating (incorrectly) on them and to make people better able to update on correct messages. (Though I'm not sure how tractable any of those things are.)
• I agree that it seems like a major risk from proliferation of misinformation, fake news, etc., is that people stop seeking out or updating on info in general, rather than just that they update incorrectly on the misinfo. But I wouldn't say that that's "the real problem with fake news"; I'd say that's a real problem, but that updating on the misinfo is another real problem (and I'm not sure which is bigger).
• As a minor thing, I think when people spread misinfo, someone else updates on it, and then the world more generally gets worse due to voting for stupid policies or whatever, that's also an externality. (The actions taken caused harm to people who weren't involved in the original "transaction".)
• I agree you can fool/mislead people without lies. You can use faulty arguments, cherry-picking, fairly empty rhetoric that "feels" like it points a certain way, etc.

I wonder if fact-checking agencies could evolve to some sort of "rating agencies"; I mean, they shouldn't only screen for false statements, but actually provide information about who is accurate

Not sure if I understand the suggestion, or rather how you envision it adding value compared to the current system.

Fact-checkers already do say both that some statements are false and that others are accurate.

Also, at least some of them already have ways to see what proportion of a certain person's claims that the fact-checker evaluated turned out to be true vs false. Although that's obviously not the same as what proportion of all a source's claims (or all of a source's important claims, or whatever) are true.

But it seems like trying to objectively assess various sources' overall accuracy would be very hard and controversial. And it seems like one way we could view the current situation is that most info that's spread is roughly accurate (though often out of context, not highly important, etc.), and some is not, and the fact-checkers pick up claims that seem like they might be inaccurate and then say if they are. So we can perhaps see ourselves as already having something like an overall screening for general inaccuracy of quite prominent sources, in that, if fact-checking agencies haven't pointed out false statements of theirs, they're probably generally roughly accurate.

That's obviously not a very fine-grained assessment, but I guess what I'm saying is that it's something, and that adding value beyond that might be very hard.