It’s reasonable to dislike GMOs (or some subset of them) because of who’s selling them and why, unrelated to the science. It’s reasonable to argue against fluoridated water even while accepting it’s good for dental health, because you disagree with mass medication. It’s reasonable to buy organic food if you know it to be free of certain chemicals which, knowing their scientific characteristics, you would rather avoid.
I think this is a pithy description of human beings. :)
Of course, it's a habit we'd all do well to do out best to develop.
In case of GMO it is a play with the unknown (health, stability), it is a risk against a somewhat cheaper food. In case of vaccine it is still a play with unknown, but there the risk is against another risk not just money. If the virus would be less deadly much less people would have taken it. And the other way around as well, would be more deadly people would queue up instantly.
It is not as black and white as you describe. stupid vs smart people as you say it.
And by the way, this is called common smartness. Everybody is susceptible for different thing everybody is resistant to different things so the whole word is hard to take on.
So yes, it is a question of people grasping the science, not of this specifically, but as a whole. They are not on-board, they never fully confront any contradictions that they encounter or spew. Logic is not their friend, they are not inquisitive, getting to the bottom of something is not in their nature. You might think that in general people are reasonable, but margins are not that high and informed-ness is very surface-level.