how do I teach them about this new world of critical thinking and data?

A phrase for this that I came across recently is 'unmediated access to reality.' That is, most things that people do are mediated by the people around them; you write an essay, and the teacher decides if it's a good essay on not based on their subjective standards. You write code, and the compiler determines whether or not there's a syntax error based on its objective standards, and there is no pleading with the compiler.

I think programming is the easiest way to get experience of living in an objective-truth-world, but it's worth pointing out that this is one of the reasons programming is so painful, and encouraging people to program because hunting for bugs is character-building* instead of because programming is useful seems like it might not go far.

*Specifically, it builds a lot of rationalist habits, and people talking about the heuristics and biases as 'bugs' in 'mental programming' seem to be making a very close analogy. I don't think it's an accident there are so many CS people running around here.