This is why there needs to be a law simply enforcing vaccination --- people cannot deal with the fear that their child will be the 0.00013% of people who might react to a vaccination..
In a study published in 2015, just 33 people had a serious, potentially life-threatening allergic reaction -- also known as anaphylaxis -- out of 25 million vaccines given. The researchers identified 380 cases of anaphylaxis, possible anaphylaxis, or allergy (0.0015%). That's still several orders of magnitude lower than a 1% risk.
About 1 in 5 un-vaccinated people (20%) in the U.S. who get measles end up hospitalised. As many as 1 out of every 20 children (5%) with measles gets pneumonia, the most common cause of death from measles in young children.
So, there is evidence that people who fear vaccination simply don't fear the risk of their children coming down with serious diseases that usually cause permanent damage to a growing child.