When the concept of vaccination was new, it was political. After a few rounds of stopping really bad disease (smallpox, polio, rabies, etc...), people mostly believed in vaccine because they literally eradicated disease. When COVID hit, I think it benefited from the reputations of successful vaccines of the past, and a lot of people put their faith in public health officials who in the past were the vanguard for eradicating some very dreadful, horrible viral diseases.
After getting couple doses of COVID vax, actually having everyone in my family (who is vaxed) including me get COVID (and some of us get seriously ill), I have a very hard time believing that the COVID vaccination was very effective, especially if you compare it to the vaccinations that have successfully eradicated entire diseases. Millions have shared the same experience my family had.
Yes, desperate times call for sometimes desperate measures, and I like to believe that the COVID vaccine helped blunt the pandemic... but the fact is people get this vaccination and still can get COVID and even die of die of it. This is the source of the cognitive dissonance we see in the body politic right now... and why trust in public health is down substantially.