There was a recent discussion about Wikipedia here recently where a lot of people who are active on the site argued against people taking the claims there with a grain of salt and verifying the accuracy for themselves.
We can teach these things until the cows come home, but it's not going to make a difference if people say it's a good idea and then immediately do the opposite.
If you mean whether Wikipedia is unreliable? That's a different story, everything is unreliable. Wikipedia just happens to be potentially less unreliable than many (typically) (if used correctly) (#include caveats.h) .
Sources are like power tools. Use them with respect and caution.
You are very optimistic.
Look at all other skills we are trying to teach in school. 'Critical thinking' has been at the top of nearly every curriculum you can point a finger at for quite a while now. To minimal effect.
Or just look at how much math we are trying to teach the kids, and what they actually retain.
Critical thinking is a much more general skill which is applicable anywhere, thus quicker to be 'buried' under other learned behavior.
This skill has an obvious trigger; you're using AI, which means you should be aware of this.
This cuts both ways. I have yet to find an opinion or fact I could not make chatgpt agree with as if objectivly true. Knowing how to trigger (im)partial thought is a skill in and of itself and something we need to be teaching in school asap. (Which some already are in 1 way or another)