Tender care for the meek anti vaxxer

[j.p.]

How would the one-trick pony respond? Oh, I know, RACIST!

Not this time. The anti vaxxer is a little simpler than a racist

#8 of Method
Deal with the anti-government conspiracy theorists. Some people who believe vaccines are bad, think so because "they're from the government, so they are not safe!" This is just paranoia. Governments are trying to keep people safe and allowing hospitals and clinics to use vaccines is just a step-in order to make sure that an outbreak of a major disease doesn't affect everybody.
Ask what motive the government could have for making people sick or disabled. Why would they do that?
Break down the argument of "sick people make them money" by pointing out that while non-disabling illness does require people to pay money, it also costs the government money to support sick or disabled people (e.g. long-term disability payments).
If a sizable portion of the population dies or is permanently disabled from vaccine-preventable diseases, that leaves fewer people who can make money, help maintain the country, or take over someone else's governmental role should they die or retire.