The measles vaccine should be mandatory - no exceptions
As a philosophical libertarian, I believe you should be allowed to do what you please provided you are not harming anyone else. This means you cannot steal someone's property, assault them or kill them. You cannot recklessly damage someone's property or endanger someone's life. But as long as your choices only impact you, the government should pretty much leave you alone.
It is based on this principle that the measles vaccine (and other vaccines for deadly diseases) should be mandatory, with no exceptions. The paranoid anti-vaccine movement has relied on crackpot "science" to spread fear, so a bunch of entitled rich people have failed to protect themselves and their children from a deadly disease. They have exploited the incredibly weak system of exceptions to put public health at risk and it is time for the government to step in and put a stop to this. If necessary, people should be forcibly vaccinated as a public health measure.
Mandatory vaccination of children is tricky. Parents should have wide latitude in how they choose to raise their children, but parental rights are not unlimited. Child abuse is obviously a crime. Parents who fail to feed their children can lose their parental rights. Because children (especially infants and toddlers) cannot make rational medical care choices, their parents must provide the proper care. Therefore, not seeking medical care after a serious injury is grounds for neglect charges. Vaccines for potentially deadly diseases fall into that category.
In addition to protecting the rights (as well as the lives) of children from foolish parents, the civil magistrate also has a legitimate interest in protecting public health. People who refuse perfectly safe vaccines can spread deadly diseases through the population, and therefore violate the rights of other citizens. Because we interact with many others on a daily basis, the state has an interest in protecting their lives and health from the foolish choices of vaccine opponents.
I am generally not one to advocate for more government. But while I am a philosophical libertarian, I am not an anarchist. While mandatory vaccinations may seem like a radical proposal, it is a reasonable one.