Our social contract demands people able to be vaccinated get vaccinated
If you fail to vaccinate an eligible child you are willfully endangering not only that child but everyone else's. This should be a crime.
The exact same reasoning applies to vaccination. There is no moral difference between a drunk driver and a willfully unvaccinated person. Both are selfishly, recklessly and knowingly putting the lives of everyone they encounter at risk. Their behavior endangers the health, safety and livelihood of the innocent bystanders who happen to have the misfortune of being in their path.
The reasons why are simple and straightforward. Vaccines aren't perfect (e.g., they can wear off over time) and not everyone can be vaccinated. There is one and only one legitimate reason to skip a vaccine: being immunocompromised. Some individuals, because of genetic deficiencies or diseases like cancer, cannot receive vaccines. Other people are too young. Vaccines such as MMR (measles, mumps, rubella) cannot be administered before 12 months of age. These vulnerable people rely on the responsible actions of everyone else in society to protect them, a concept known as "herd immunity."
For their sake, we have a moral-and there should also be a legal-obligation to protect them. Everyone who can be vaccinated must be vaccinated in order to prevent the spread of disease. This is a protection we demand even for our animals: kennels will turn your pet away if they aren't properly vaccinated and on an accepted flea treatment. There are rules we all have to play by and responsibilities we have to live up to if we want to live in a society together.
If this isn't enough to convince a person to become fully vaccinated, then perhaps there is a solution that maintains everybody's freedom: Anti-vaxxers can opt out of American society. No public or private school, workplace or other institution should allow a non-exempt, unvaccinated person through their doors. A basic concern for the health and safety of others is the price it costs to participate.