I think that much of the distrust is not so much caused by lack of knowledge, but ultimately by inability to accept that sometimes shit just happens. They spent an entire year frantically making up culprits to blame for a virus that quite likely just happened, like a meteor strike. Making up culprits from thin air, but decidedly. Because their minds had never been confronted with tragedy lacking a scapegoat.

There's no logic to go from there to "vaccines are bad", but all the mental contortions they had to go through to blame someone primed them, hard, to active distrust.