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Someone is interested in laws regarding vaccination in the United States. There is often a tension between the liberty interest and social welfare in public health, at least from many people's perspective. It is a general principle that competent adults cannot be compelled to undergo any medical procedure against their will. Adults can decide to check out of the hospital against medical advice, or to treat their cancer with coffee enemas rather than surgery and chemotherapy, and the state does not get involved. As for people who are ruled not competent, that's a whole other discussion, but I will point out that a judge has to make the ruling; psychiatrists can't just do it by themselves.

Vaccination is a different matter for two reasons. First, we are talking for the most part about children. While laws, precedents and practices vary somewhat among the states, generally speaking parents can be compelled to allow essential medical treatment for their children, and may be prosecuted for neglect if they do not. There is ample precedent for compulsion to overrule even religious belief in this regard.

However, because not getting your children vaccinated is not under most circumstances immediately life threatening, the states do not directly compel it under normal circumstances. Rather, they require vaccination for school attendance, the rationale being more that it is about the protection of others rather than protection of the subject child. And most states allow religious and/or personal belief exemptions, which makes this more of a suggestion than a requirement. The map below is a couple of years old and some states may have changed their laws since, but it gives the general idea.



So only California, Mississippi and  West Virginia (perhaps surprisingly) do not allow any non-medical exemptions. There isn't really any difference between religious and personal belief exemptions because all you have to do in either case is assert that you have such a belief.

In the case of the recent measles outbreaks in New York, the Public Health Commissioner declared a public health emergency and required  everyone -- adults and children -- who lives or works in the affected zip codes to be vaccinated, subject to a $1,000 fine. I don't know what the law is regarding such measures in other states but the courts have generally held that state authorities have very broad authority to protect public health under the police power. This includes measures such as isolation and quarantine which are even more coercive than requiring vaccination, which in fact constitutes an extremely low risk which is far outweighed by the benefits. That's the scientific truth, and people who don't believe it are simply wrong. It is not subject to debate by reasonable people.

I don't know what your average libertarian thinks about this but I expect most of them do not want to be exposed to infectious diseases. The measles vaccine is highly effective, but vaccines in general are less than 100% effective so you need to vaccinate almost everyone to achieve "herd immunity." That means that the infectious agent cannot spread because it will not encounter long enough chains of transmission. And, since some people cannot be vaccinated for medical reasons, they will be at risk due to the indefensible decisions of others who decline to be vaccinated.