While I do believe that there are certainly valid and reasonable arguments for anti-vaxxers which are also grounded in scientific basis, I still believe that in cases such as these where the rights of one person places the health and safety of tens of thousands of those in their proximity–and possibly even millions of people if the disease or virus is not properly dealt with– government intervention is most definitely justified. It is a common understanding that certain rights can be withheld in cases where the practicing of those rights endangers others; for instance, the freedom of speech, which is a fundamental right, can be withheld if those words hold an inherent malicious intent and have the capability to cause harm (i.e. bullying and death threats). I believe that the same logic applies here. Of course, it is of paramount interest that everybody's right is guaranteed, and while that may be possible in a utopia where there are no clashing interests, reality is riddled with situations like these in which two parties have opposing viewpoints.
Furthermore, as citizens of a nation and members of a society, from the moment we are born, we are automatically signed into a social contract. In this intangible contract, we are expected to act in civil ways in exchange for being part of a society. A common understanding of what it means to be "civil" is to consider other peoples' interests in addition to considering ours. By this logic, acts such as stealing, trespassing, battery, rape, and murder are all considered "uncivil" and therefore unlawful, because they do not take into considerations the interest of the greater society. Vaccines are no different; by ensuring that one's child is both safely protected from diseases and does not endanger others of the disease, individuals place the wellbeing of the society above their personal beliefs.
All of this being said, it is understandable that many still fear vaccines and have a certain perspective when it comes to injecting their children with weakened bacteria and viruses. Thus, it is also the role of the society as a whole to build trust within those select individuals and properly educate them about the benefits and importance of keeping their children safe and vaccinated.