That is a strawman argument which brings nothing to the table. And on this topic, Dr. Paul ISN'T wrong. We all have the right to informed consent for medical procedures and as parents are 'responsible' for their infants health, THEY then have the right to informed consent on behalf of their infants.
You mention a "parent's ignorance" .... well, would it surprise you to know that the more education parents have the more likely they are to withhold vaccinations from their children? We don't do it BECAUSE we're ignorant--quite the contrary. We do it because we have done the research--and that research suggests that there is just as much risk of harm from the vaccines as there is "benefit" to using them--not to mention the use of objectionable materials in the vaccines (such as the use of aborted fetal cells).
Knowledge is power and we exercise that power by CHOOSING to not vaccinate. Comparing that to exposing children willfully to radiation or some other harmful element is just not productive.