First of all, it is somewhat harsh to use the word “ignorant” to describe people who do not wish to have their children vaccinated. It is easy to argue that they are mistaken in their beliefs, but the word “ignorant” implies a sort of inferiority that we should not attribute to them. On the other hand, if you mean "ignorant of the facts," meaning uninformed, you must clearly say so.
To argue that these people are mistaken, we should point out that the vast weight of scientific evidence points to the idea that vaccines are safe. There are people who claim that vaccines cause autism or that they cause other mental problems, but these claims have not been substantiated in a scientific way. Someone might say, “my child got Vaccine X and then became autistic,” but that is not the same thing as proof that vaccines cause autism. This is an example of the fallacy that confuses association (Thing B happens after Thing A) with causation (Thing A actually caused Thing B to occur).
These beliefs are prevalent to some degree because of current suspicions of science and because parents are naturally very concerned for their children’s welfare. It is important to try to educate people about scientific findings, but it is also important not to condemn them as “ignorant.”