I swear, some people would just totally disband the government and condone total anarchy if they could.
Considering vaccines prevent mass outbreaks of deadly diseases, I think that far outweighs the possible side effects. It's the government's job to protect its citizens - if people don't get vaccinated, then not only do they put themselves at risk, but also those around them who don't have the vaccine. Since vaccinations have become routine, we've totally eradicated smallpox, and other diseases such as polio are practically unheard of nowadays. Requiring those shots prevents practically the entire populace from contracting those deadly diseases.