I was going to include a few links to recent reputable studies which confirm exactly my talking points, but why - they are very easily found, trivial outcomes that have been proven time and again and I’m not here to do throw chicken bones to people that form counterpoints on emotion.
I don't think that studying science leads to increased critical thinking until the point where you're having to actually discover things for yourself - because before that point you're just re-learning what other people are telling you is true.
With respect to the association between engineers and extremist groups and beliefs, I would wager that this is probably better explained by a third factor (personality traits which make someone less flexible, and less comfortable with shades of grey, for example).
Your comment is interesting, but none of the questions it raises mean that what I said wasn't true.
The question is not "are engineers inherently better thinkers". The question is "If you take someone and teach them STEM topics, do they become better thinkers than they were previously". The answer is (ironically / speaking of black and white thinking) pretty unequivocally "yes".
The effectiveness of STEM education is certainly held back by the difficulties in keeping students engaged and interested, and in the failings of the educators themselves. I would suggest that raising the bar for educators (assuming supply wasn't an issue, which I recognize it is) would go a long way towards teaching STEM better, and augmenting its impact on students' lives.
Edit: I did learn about epistemology in school, but coverage was rather superficial and incomplete. I suspect people's experiences vary wildly.
This claim that the world would have less conspiracy theorists if only there was more science on the curriculum at school has a huge [citation needed]. So much of that stuff is downwind from cultural conflict and distrust of the government, not a lack of education.