dangerously idealist. (even if there is discussion to be had about scientists losing credibility, where i'd put forward the case that a lot of the time it's intertwined with the way politicians and non-scientific experts like economists have spunked away their credibility)
science didn't beat religious fervor by debating them to death, it won because (1) it actually worked. "god's on my side!" doesn't count for for much when you're taking a sword to a gunfight, and (2) people were compelled into getting vaccinated or otherwise complying with such directives. (even if, by modern standards, the level of compulsion may seem benign. consider, for example, the way that men in WW1 were press-ganged into the trenches before
generalized conscription by "mere" social pressure.)
repression and the use of force is always the name of the game. there was never any mystical time where ordinary people were converted to the scientific method (or any other worldview) by reasoned debate. that was always an illusion caused by the fact that for a period, the entry costs to mass publication were so high that official censorship was of limited necessity. (and even then, unofficial, private censorship was rampant.)
there is surely an essay to be written about the rise of antivax nonsense correlating with neoliberalism, a worldview that puts the market above the public to the extent that the freedom of grifters to sell lies and placebos is considered more important than the public's freedom from the plague. if you want your root problem, that's where it lies.