Linking this anecdote to anti-vaxxing really seems a stretch, and I would like to see the reasoning behind that. My impression is that anti-vaxxers have more issues with vaccines themselves than with doctors who recommend them
“Asking inquisitive questions and thinking for themselves? Must be an anti-vaxxer!”
They are closely related. The authority of the medical establishment is more and more questioned. And whenever it is correctly questioned, they lose a bit of their authority. It is only their authority that gets people vaccinated.
"My impression is that anti-vaxxers have more issues" - I think you could have left it at that!
I think that completely misreads a comment that was already painstakingly clear, they're specifically talking about the phenomenon of reasoning by anecdote. It wasn't a one-to-one equivalence between LLM driven medicine consultations and the full range of dynamics found in the anti-vax movement. Remember to engage in charitable interpretation.