So as you learn more and more facts and see how interwoven they are you're able to evaluate further information without having to base on trust alone. If, say, vaccines were harmful or synthetically produced compounds were somewhat "toxic" compared to the same compounds found in normal food, you'd have to literally throw half of your scientific knowledge away. So you can easily determine that those claims are bullshit. But that requires knowing relatively lot of stuff, which majority of people do not. They have to rely on trusting authorities - which keep lying all the time. So no surprise here that people just don't believe science or government and are drawn towards various pseudoscientific nonsense that is presented as contrarian and promoted by charismatic individuals.
Exactly. When you know enough science (which will likely require you to be biased towards it, as otherwise the education system will make sure you don't learn any of it) things start to increasingly fall into place. You'll see that the whole body of things you know is internally consistent. It has to be, because the reality itself is.
In that context how is it possible to convince someone that science is not also as corrupt as every other institution they've encountered. If my entire experience of education is that it is unfair and run by sadists, then the only people who will succeed in it are those who are willing to subject themselves to what they are told. Their perspective is built into their environment.
These skeptics and deniers can't be convinced, but not because they are stupid. The entirety of their lives lead to the subjectively rational conclusion that everything they are told to do will keep them miserable so they believe and do none of it.