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Basically, I think that rabid anti-vax sentiment is a natural conclusion to roughly ~40 years of near-constant levels of conspiratorial thinking from conservative circles. I think folks like Jerry Fallwell started it, and subsequently Ronald Reagan and most of the conservative politicians after him followed. People like Jerry Fallwell more or less started the "satanic panic", and it started to become somewhat politically acceptable to just say that "the devil" was doing anything that they don't like. This went largely unchallenged in evangelical circles and the evangelicals took a huge turn towards the Republican party.
Fast forward to 2012, and now it's a debate about where Barack Obama was born. A "conspiracy" was just fabricated out of nowhere, and the president is required to show his birth certificate. This was somewhat made fun of, even Bill OReilly disputed it, but it was the first conspiracy that I had heard in my lifetime being taken seriously by at least some politicians.
Fast forward to 2016, and suddenly it seems that idiots like Alex Jones, who had previously been a goofball I would turn on to get a laugh, is being taken seriously by semi-prominent conservatives. PizzaGate was still somewhat of a fringe thing, but it was the first outright debunkable conspiracy that I could think of that people I actually knew who actually believed it.
Fast forward to ~2019, and a sizeable chunk of conservatives (to be clear, NOT a majority) were starting to take the QAnon nonsense seriously, setting the way for 2020, which allowed a basic stream of perpetual lies about COVID to be spread (and accepted) on 8kun. Suddenly, despite overwhelming evidence, we have to have debates on whether we should be taking COVID seriously. Any time Fauchi contradicted Trump, it was because Fauchi was an agent of Satan or something absurd.
I think anti-vaxxing is just the natural progression. There's been an entire generation who has been more-or-less unchallenged in their conspiratorial thinking, and basically anything can be a conspiracy theory. Since they already think that COVID was overblown to make Trump look bad, they subsequently have to think that anything that addresses covid must also be bad.
The left has its share of dumb things that it believes, but it's not nearly at the same level of what is predominant in conservative culture today.
While schools definitely do have a lefty-bent, the idea that it's some hyper-organized society designed to destroy the conservative parties in America is absurd to anyone who isn't predisposed to conspiratorial thinking.