Some vaccinations should be mandatory
I am a philosophical libertarian, so my basic philosophy is this: Unless what you do harms another person, then you should be allowed to do or not do what you please. I also believe parents' rights should be respected by the state. The authority to raise children resides naturally with the parents, not the civil magistrate.
However, I do not believe these rights are unlimited. I am not an anarchist.
We have seen multiple outbreaks of measles due to various populations refusing to vaccinate their children against the disease. Measles is a serious and potentially deadly disease, and is highly contagious. The very young, the elderly and people with compromised immune systems (such as cancer patients) are especially vulnerable. When people refuse to vaccinate, they are putting these lives at risk.
If you live on an island with no contact with the outside world, refusing to vaccinate is one thing. You will not be spreading the disease to other people. But in an incredibly connected world, that is not the case. Anti-vaxxers cause real harm to innocent people. To prevent this harm, vaccinations for certain diseases (specifically for measles and chicken pox) should be mandatory.
I understand this is an emotionally charged issue, and I understand the precedent this sets for further infringement on parental rights. The state wants to absorb all authority for itself, and we should be wary of that. It certainly should not be mandatory to vaccinate children against sexually transmitted diseases. But things like measles represent enough of a public health risk that it is time for the civil magistrate to step in.