Much of the modern anti-vaccine sentiment stems from the controversy and subsequent fear-mongering over the preservative thimerosal (which contains mercury) in the 1990s. While the CDC and FDA still maintain that there is little danger in thimerosal - including NO link to autism - they asked vaccine mfgrs to voluntarily stop using it in 1999. Then in 2001, it was removed from any vaccine targeted to children under age 6, except for some flu vaccines.
FWIW, autism rates continued to rise even after the removal of thimerosal from vaccines, giving further evidence of a lack of any causal link.
https://www.cdc.gov/vaccinesafety/concerns/thimerosal/index.html
https://www.fda.gov/BiologicsBloodVaccines/SafetyAvailability/VaccineSafety/UCM096228
https://www.epa.gov/mercury/thimerosal-vaccines
http://www.immunize.org/thimerosal/
Once again, everyone has to realize that ANY substance has the potential to trigger a hyper-allergic reaction in a VERY small percentage of the population.
Also, FWIW, I understand the separate controversy over the [lack of] efficacy of the flu vaccines. Flu vaccines are by their very nature designed for last year's strains, and cannot accurately predict what's going to evolve this year. I am less interested in those who object to what amounts to an annual experiment, than I am in those who renew baseless objections to vaccines that have been proven over decades.