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.

Yep, maths and science are only partially about learning maths and science. The even more important purpose is learning critical reasoning skills, which is a requirement for media literacy.

I'd say critical thinking is divorced from any one subject. You can learn it in a humanities context just as easily as a scientific one.

I think the flip side of this is Facebook or wherever the link was pushed to your in-laws (which is what I'd guess happened) feels... empowering. Those apps are literally optimized, with billions of dollars (and extensive science, especially psychology), to validate folk's views in the pursuit of keeping them clicking. Their world's telling them they're right; of course your retort will feel offensive and wrong.

They're in a trap.

And I still see lot of scientists posit 'why is this happening?' unironically on Twitter or something, which really frustrates me.

I'll provide a non-western perspective on this:

My mother was born in mainland China, according to her, doctors were corrupt and would prescribe unnecessary medications or perform unnecessary medical procedures because the doctors were incentivised and get more money by doing so.

That's why now in the US, he maintains the same beliefs, reluctant to let me get antidepressant medication, because she see the as "crutches", unnecessary "happy pills" for "weak" people, "too many side effects", "harmful for health", "these doctors probably don't know anything", "it's all in your head".

It goes far as: "try this necklace that repels evil", wtf lol.

Also: Fucking Wechat and the fucking "herbal medicine"/TCM or whatever🤦‍♂️

It's not a new thing. The same issues were the case for television, radio, and newspapers. They had to teach media literacy before the internet too. You go back into the archives and you'll see some wild misinformation that's very reminiscent of what we see on the internet. We did have a brief few decades where we had a more consistent and adhered to set of standards, but these were by no means universal. The perception of reliable information is also skewed the combination of being less aware of misinformation when younger and by a unique period where mass reputable media were all saying the same thing... But that also meant they were leaving the same things out.

But the internet did change things. Standards have been blown up, misinformation is much faster and the volume of it is much higher. Our brains couldn't keep up with 24hr news channels, let alone the cesspools of social media we have now.

It is clear, you need some bases to be able to reasonice and understand the cause of an problem. You can find the cause of an problem why an engine don't work with some basic knowledge about physics, but even an intelligent aborigen who has no knowledge about mecanics and physic never can, also not a person which only had memorized data without understandig it, can't But the current education system priorice the latter, because of this there are a lot of integral idiots with graduation, which outside of their routine don't understand anything.