I don't knock street smarts, and I do believe in living by your gut. I think people without formal education or much numeracy will - left to their own devices - come to very sane conclusions about viruses and vaccines if they're just given the raw data to work through. What they don't have is the armor to repel false arguments. The premise of telling someone who's never read a medical text to "do your own research" - by reading conspiracy sites online - is just so ridiculous that you know whoever is telling them that is laughing up their sleeve. I live in a deep red area so I see this all the time... when people say they did their own research on the vaccine, I think, wow. Research is a big word.
This is different from having a gut feeling that something is wrong and you don't trust the government. It's almost like the in-group of pro-vax, pro-science liberals has deliberately organized and promoted a mass display of ignorance by the skeptical country folks just for the purpose of pointing and laughing and delighting in their ignorance. And yet, the antivax fever that's swept over the red states is still ignorant, and even more so if it plays directly into a concerted plan to make them look like fools who are prolonging the pandemic.