Ask a COVID anti-vaxxer to explain their position, and it will almost immediately include at least one outright falsehood. Not a "difference of opinion" or "interpretation" or "risk tolerance", but just an outright lie. And correcting that will not result in any reconsideration of their stance.
Most people don't really understand any of the vaccines they're taking, but they put their trust in a medical system that has largely justified that trust. Some people have suddenly decided to disagree with the entire scientific and medical establishment, seeking out specific individuals for their ideological agreement.
There is a large difference in trust, but it's not founded in science. It's founded in a bias, and that's dangerous.