When a parent chooses not to vaccinate their child, they put many other people at risk. Some infants cannot be vaccinated due to medical complications, and even fully-vaccinated people are not always fully protected. Jessica Parsons tells the story of baby Finn on Aetiology, who was diagnosed with Ewing’s Sarcoma at the age of 3 months and has been undergoing chemotherapy, surgery, and blood transfusions ever since. Because he was immunosuppressed, Finn could not be vaccinated, and despite responding well to cancer treatments, his life was imperiled by a case of whooping cough. Meanwhile, on ERV, Abbie Smith explains that vaccination against measles does not guarantee that you will not contract and even transmit the disease. But 87% of measles infections in 2011 in the U.S. occurred in unvaccinated individuals. These are the people keeping antiquated pathogens in circulation, endangering the lives and well-being of others.
Here in California, we have anti-vaxxers across the political and religious spectrum: in liberal Marin County, and in conservative Orange County, among Evangelical Christians and among New Agers (I haven't heard of it going around among atheists). Most common forms of conspiracy theory (e.g. 9/11 CT) merely cause impaired thinking, but anti-vaxx CT causes real disease and death.
As it turns out, there is not a Constitutional requirement to offer religious exemptions: only a Constitutional requirement to treat all religious claims as equal under the law. Thus, city governments could, if they chose, completely disallow any and all forms of religious exemption (thereby treating all such claims equally under the law), and only allow actual medical exemptions (e.g. kids who have egg allergies, compromised immune systems, etc.). Private employers can do likewise by insisting that all of their employees (and arguably employees' families) get their shots, medical exemptions only.