Your question is framed in a way that, at least as it appears to me, has a bit of your opinion mixed into it. If that's true, I agree with your Devil's Advocate point that shunning parents or labeling 'Anti-Vaxxers' in general as an uneducated or ignorant group is pretty counterproductive. To them, the most important part isn't that science is backing their argument, but that morality is. They strongly feel a victim mentality as the minority of society, which, as backwards as it is, is their own justification. That is, they feel they are justified as they are the minority themselves, so it is the might of the majority and their 'ignorance' that is wrong. To tackle this isn't to shun them, as it only furthers their inherent moral justification.

How can I be sure the majority hold a moral justification? As a poster said above, they ignore scientific evidence, or exist in their own echo chambers–they hear only what there is to justify themselves. But this isn't all to say that I think there is no way to reverse the thinkings of 'Anti-Vaxxers'. In my mind, the best way is to simply present the harms as best as possible (education, advertisements, etc), and publicly present individual, specific cases (as this makes each of them feel more human, more relevant) where not vaccinating a child was the direct result of severe lifelong disabilities or death. This is really learning by themselves, and gives them that illusion of freedom of choice that makes them realize that, no, they aren't the victims after all.

I feel as if parents who choose not to vaccinate their children should be shunned in some ways. I definitely think that this approach, however, is not effective in ensuring that as many kids are vaccinated as possible now and in the future. Most anti-vaxxers rally behind the false cause that vaccines cause autism or other ailments. I think you are right in that if this continues, more parents may start to go against the grain and refuse to vaccinate their kids. If information and the dangers to not only their child, but also every child around them, is distributed more frequently and publicly, we may be able to convince some anti-vaxxer parents that they are doing their children and the children of the future a major injustice.

Although it may not be the most positive response, I believe that people's responses to those who aren't vaccinated is justified in many ways. In the privileged, modern society that is the United States, it comes as a shock to many that people optionally deny medical services that aren't available in many other countries. Also, oftentimes anti-vaxxers justify their decision with responses like, "Vaccines cause autism", but don't or can't back it with any scientific evidence. It can, and often does, come across as ridiculous. There exists a frustration with anti-vaxxers because oftentimes they understand the numerous benefits of vaccines and how privileged they are to even have the option to be vaccinated, but still find a way to justify their stance.