And I deliberately did list MKULTRA in an attempt at steelmanning, because sometimes the tinfoil hat crowd are right. The problem is not what conspiracy theorists believe per se, but rather the methods by which they come to believe it, because those methods are not the most useful in understanding the world. In fact, they're worse than useless: they're actively toxic to having a framework for processing information that leads to believing as many demonstrably true things and as few demonstrably false things as possible.
The focus on plausibility over provability is a prime example. For one thing, the universe is provably implausible, but more importantly, your understanding of what is plausible is internal and subject to shifts in how you think. If you always think they are out to get you, that will feel more plausible to you, and you will start to see more evidence for it even if you have to bend it to fit. Moreover, other assertions with similar traits will also seem more plausible, which is how crank magnetism happens. Go far enough, and it becomes an implicit assumption that "they" planted all the contradictory evidence and hid all the proof and bought all the experts, at which point one can believe anything. It gets easier to operate in the realm of "isn't that interesting" and "what would we expect to see? exactly this" without all the fiddly checks and controls and other considerations, and it eventually soaks into your identity. Spend long enough thinking conspiratorially, and eventually all the experts have to be wrong, or else you're a fool who has wasted a ton of time on nonsense.
"Hard evidence" is great, but without a rigorous framework for defining for what it is supposed to be evidence and what other evidence would influence the probability of that theory being useful, it's just information, and can fit whatever pattern you want. "Critical thinking" is a fine idea, but without logical clarity it devolves into just casting aspersions on the credentials and motivations of anyone who disagrees with you. What our culture is evolving to do is to find ways of making reflexive, emotion-driven distrust sound smart to other people who don't know better, and conspiratorial thinking is leading the charge on that.
It sounds absurd, and I'm sure some smartass is going to put this in the quotes thread, but just because something happens to be true is not sufficient reason to believe it. Unfalsifiable things can be apparently true, as can things that aren't quite supported by the data but are concordant with it, and it's that latter that conspiracy theories evolve to run on. Believe in things only to the extent to which efforts to falsify them have returned confirmatory evidence, and then only with precision that borders on paranoia, because that's the last point at which one can stop before the slow slide into believing absolute nonsense.