IMHO, understanding the Scientific Method and, maybe more importantly, why it is as it is (so, understanding things like Confirmation Bias - including that we ourselves have it without noticing it, which skews our perception, recollection and conclusions - as well as Logical Falacies) is what makes the most difference in how we mentally handle data, information and even offered knowledge from the outside.

PS: Also more broadly in STEM, the structured and analytical way of thinking in those areas also helps in things like spotting logical inconsistencies, circular logic and other such tricks to make the illogical superficially seem logical.

Even subtle but common Propaganda techniques used in the modern age are a lot more obvious once one is aware of one's one natural biases and how these techniques act on and via those biases, purposefully avoiding logic.

Personally I feel that that's the part of my training in Science (which I never finished, since I changed the degree I was taking from Physics to EE half way) is what makes me a bit more robust (though not immune: none of us are, IMHO) to Propaganda.

Science is powerful but, as you've stated, balance is most critical. It was one of the most impactful biologists of the modern era that wrote "the civilised races of man will almost certainly exterminate and replace throughout the world the savage races" based on his theory of natural selection.

As you can imagine, statements like these were used to justify the Atlantic slave trade, the genocide of indigineous people ie. "manifest destiny" and other colonial era horrors.

One should not treat science or the words of scientists as absolute truth. Unfortunately it is not free from human greed or corruption.