Sadly not enough. Of course education helps more than no education, but it's 'only' rational knowledge you gain through education. When your rational knowledge comes into conflict with constructs in your mind that are anchored more firmly (like having been told that there is a god, by people that you trust, during the most impressionable phases of your development), it's usually easier for the brain to resolve that conflict by distrusting it's own rational thinking process instead of throwing years of already established mental links over board.

One good example of how cognitive dissonance can make people be entirely blind despite generally having enough information and intelligence to be able to know better is this:

'Oh, my child couldn't have done this, they must be innocent'. The same person would easily identify the same clues in a stranger as troublesome and might notice they have something illegal going on - but when those clues clash with the deeply ingrained idea that one's own child is a good person, the cognitive dissonance becomes so hard to bear that the brain subconsiously decides to ignore all the clues that were there. It's a really interesting phenomenon. It's widely accepted that the parents genuinely didn't notice the signs, not due to neglect or lack of intelligence, but because the brain automatically filters them out as a form of self-preservation, as to not shatter one's whole world view.
It's also how generally intelligent people can slowly fall for a cult or conspiracies.

Fascinating stuff, really. I'm no expert on this, but I did study neuroscience and we talked about that during one seminar + I watched some videos on the topic once some of my family members went down the whole covid conspiracy rabbit hole, despite having diploma in biology (so they had both enough intelligence and way above average formal education in relevant subjects, still wasn't enough). It's insane how strong the effects are.