As long as there have been vaccines, there have been people who doubted their science and safety.
Back in 19th-century England, people rioted against a mandatory smallpox vaccine, claiming that it violated civil rights and was an affront to human bodily integrity. In the United States, organizations dedicated to resisting vaccines have existed since the Anti-Compulsory Vaccination League of Brooklyn was established in 1894.
Researchers generally refer to people who do not follow the standard advice of health professionals about vaccines, by either refusing or delaying some or all vaccines, as vaccine hesitant. Today, vaccine hesitancy is most famously associated with the Make America Healthy Again movement and its standard-bearer, Health and Human Services Secretary Robert F. Kennedy Jr.
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