The Science didn't change that much (viz: masks in healthcare since forever), but the flip-flopping with messages ("don't horde masks; they won't save you!", "wait, no - everyone needs a mask!"), which was really less about The Science than about different concerns (mask effectiveness, availability) were just the "I told you so" they were looking for.
"Changing advice" is to be expected, but it was the outright lying, as proven by FOIA'd emails, which understandably shook faith.
I was tasked with measuring the water resistance of a proposed environmentally friendly paper coating.
I asked my supervising scientist what numbers I should expect to get back from the experiment. I distinctly remember my surprise and thrill when he looked at me and said "I have no idea, that's why you're running the experiment".
It was such a new concept to me! A scientific experiment where the correct answer wasn't written in a teacher's lesson guide, or even known to anyone!
The science mouthpieces (aka media and government speaking on behalf of scientists) were insisting they knew the immutable facts and any questions or doubt in those immutable facts were heretical. Anyone who has an appreciation of the evolving nature of scientific research should immediately see the red flags in that.
"Antivax" is not a position of anti-science, it's a slanderous label for an alternative theory with its own compelling evidence.
My theory is that in primary and high schools, science is taught as a series of immutable "facts". You get tested on remembering them, and when you do an "experiment" you get marked down if your reading of the litmus paper isn't 4. No sense of doubt, and no exposure to the epistemic boundaries to controleld trials, measurements, etc.
If your takeaway is that scientists uncover and explain immutable facts, hearing them say one thing in January and another in June can in fact shake your beliefs in these scientists.