I'm really happy to see that someone else sees this. I've been harping on this for a long time -- that the reason people believe things like anti-vaxx propaganda is not because they are idiots but because scientific authorities, the media, and the medical establishment have not earned their trust.
People subscribe to kooky conspiracy theories and fringe/quack medical ideas because those advancing those points of view appear more credible than our society's institutions. Much of that appearance of credibility is by default -- it's more that our institutions have ruined their own credibility by being overconfident or in some cases actually deceptive. I personally think it extends way beyond medicine. When the president tells us we're invading Iraq because it has "weapons of mass destruction," and that turns out to be almost entirely hot air, should people be considered stupid for suddenly trusting Alex Jones more than they trust the POTUS?
Trust is hard to earn and easy to squander. In addition when you have someone trust and then stab them in the back, the emotional reaction from that is far worse than if you never had any trust to begin with. Betrayal inspires some of the deepest negative emotions.
Edit:
Another phenomenon that I think is at work, especially with people like Alex Jones and wacky conspiracy theories, is a kind of "fuck you factor" that they have. Believing such things and perpetuating them is an act of (often subconscious) protest -- akin to things like calling yourself a "Satanist" in protest against fundamentalist religion. You might call these kinds of things "protest beliefs."
I have a friend who leans toward the view that we didn't land on the moon. He's a very intelligent person. I personally believe -- and I've told him this -- that this "belief" is more of a big fuck you to the backward-and-sideways direction NASA and America in general has taken post-Apollo. "Fine then... if you're going to cancel visionary projects so we can have more war and tax breaks for the financial industry, then I'm going to deny that you ever did it in the first place to spite you." He didn't really deny that, just kind of shrugged.