All those people who claimed to get autoimmune problems after the vaccine, must have been people who went to quite a bit of trouble to get the vaccine in the first place, so I'm not so sure it can all be written off as health panic.
This exact pattern has been playing out with the COVID vaccine and the HPV vaccine. There are communities who are convinced that every medical problem they had since receiving the HPV vaccine is due to the vaccine, even though they’re all having different health problems that also occur in the overall population.
As I said, these are people who went to some effort to try a novel vaccine. If they do that, I think it's unlikely that they are anti-vaxxers. Presumably they'd also know - or would be told - that the vaccine can't be expected to work on any post-Lyme symptoms you already have.
Of course you can just say they didn't investigate it enough or whatever, you aren't trying to make a reasoned argument and thus don't need to exercise reason.
Unfortunately vaccine-denialists will say 'ah this person died from getting a vaccine, we shouldn't vaccinate anyone'. Even if the vaccine saves millions of lives.