Distrust of authority vis-a-vis vaccination programs easily predates the 60s. There are plenty of media articles laying out the notable parallels between the themes underlying resistance to smallpox vaccination programs in Victorian Europe and what we've seen playing out over the past several years: violation of personal freedom for the sake of the collective, distrust of established sources of information and perceived elites, vaccine ineffectiveness, vaccine toxicity, and then further into conspiracy theorization. Sound familiar? Indeed, if you look at the articles below you'll see that the memes of that period were far superior than the memes of today. And some of the resistance was well founded. Jenner-era cowpox vaxx definitely had risk.
https://www.bbc.com/news/uk-england-leicestershire-50713991
https://www.washingtonpost.com/history/2021/11/14/smallpox-anti-vaccine-england-jenner/
There are scholars who get right down in the weeds about the similarities and differences between then and now with respect to vaccine resistance movements. My takeaway is that the politics is pretty much the same, but the class/sociology stuff has differences. And, of course, history keeps rolling along, the big storm never comes, and smallpox is gone.
https://pubmed.ncbi.nlm.nih.gov/11624425/; this one is kind of from what I take to be the horse shoe left
https://pubmed.ncbi.nlm.nih.gov/21770225/; and this one is kind of a straight up logical positivist analysis.