People in everyday life are not evaluating rules. They evaluate cases, for whether a case fits a rule.

So, when being told:

"Which card(s) must you turn over in order to test that if a card shows an even number on one face, then its opposite face is blue?"

they translate it to:

"Check the cards that show an even number on one face to see whether their opposite face is blue and vice versa"

Based on this, many would naturally pick the blue card (to test the direct case), and the 8 card (to test the "vice versa" case).

They wont check the red to see if there's an odd number there that invalidates the formulation as a general rule, because they're not in the mindset of testing a general rule.

Would they do the same if they had more familiarity with rule validation in everyday life or if the had a more verbose and explicit explanation of the goal?

I've confidently picked 8+blue and is now trying to understand why I personally did that. I think that maybe the text of the puzzle is not quite unambiguous. The question states "test a card" followed by "which cards", so this is what my brain immediately starts to check - every card one by one. Do I need to test "3"? No, not even. Do I need to test "8"? yes. Do I need to test "blue"? Yes, because I need to test "a card" to fit the criteria. And lastly "red" card also immediately fails verification of a "a card" fitting that criteria.

I think a corrected question should clarify in any obvious way that we are verifying not "a card" but "a rule" applicable to all cards. So a needs to be replaced with all or any, and mention of rule or pattern needs to be added.

It also doesn't explain why people don't think it necessary to check the 3 to make sure it's not blue (which it would be if "if" meant "if and only if").