If there were some sort of massive screw-up on safety procedures for vaccines, and thouands of people get injured from some horrible side-effects, you might see a much stronger anti-vax movement, turning against vaccinations generally, not just the one that caused all the trouble.
Granted, thalidomide(as far as I know) didn't lead to a major backlash against anti-nausea medication, but given that in OTL there is already the basis for a populist anti-vax movement, then having an actual mass tragedy around vaccinations might very well exacerbate that.