I don't necessarily see vaccines as a left right issue. Most are focusing on whether or not vaccines are "safe". Any medicine or medical procedure has risks. (Even giving birth is risky). Most of the medical community agrees that the medical benefits of vaccines outweigh the risks. If you were to simply ask me if people SHOULD vaccinate their children, I would say yes.
However, I have a problem with the idea of the government enforcing a medical procedure (even a minor one) onto anyone. Even more so when the arguement most used has nothing to do with the individual getting vaccinated, but herd immunity, "the good of society".
In China women were forced to have abortions, because population control was important "for the good of society."
If we allow that kind of logic to impose on the individual, it can become a very slippery slope.