These are weasel words. The antivax movement among progressive west-coast parents in the US has been covered frequently in the national media e.g. https://www.nytimes.com/2019/02/06/us/measles-outbreak.html
> The people not getting vaccinated are the people who have dealt with the government the most.
This is also not true. They're mostly people with low educational attainment who are more susceptible to misinformation, but I can see the narrative you're trying to create!
> In fact, swallowing wholesale the narrative by people who have a vast history of lying(or no history of any truth/intelligent ideas) is the least intelligent thing one can do.
Good governments generally understand this, and the most effective health policy during the pandemic was to give the mic to the scientific community.