Physicians have to be respectful of patients' choices. Choosing not to vaccinate their children is a very common reason for "discussion". Personally, I don't get angry when I speak to parents about this. Usually you can tell in a few sentences whether they even want to hear the evidence or whether their mind is made up before entering the room. The former can be a nice give and take about the controversies surrounding vaccination and the studies that back its implementation. The latter can be painful and fraught with frustration. All I try to do is give the information and be as nonjudgmental as possible.
I believe this will all change in the future. New information is coming out about how measles is on the rise (the highest level in over a decade). Measles usually is not a killer so no one is getting scared yet. The one that is going to get parents freaking out, however, is polio. Though not a huge killer either it does leave major handicaps on its prey. I am old enough to remember playing Little League with a kid who had the effects of polio. He was actually a lefty pitcher and it made his curve ball pretty amazing. But that's not the point.
Polio is rising in India and Nigeria. Many Americans go abroad and come back. Though this travel pattern is nothing new, what is new is that our strength of "herd immunity" is decreasing. When increased perpetuation of Internet rumors about vaccines meets more and more parents checking inappropriate sources, there will be sudden tipping point leading to even much more unvaccinated kids. That is when Nostradougus predicts polio will start showing its ugly head back here in America. You heard it here first.