Oh boy, this sure is a controversial topic! In my opinion, there is no credible evidence linking vaccinations against any serious effects (other than those rare ones listed on the CDC's handout for each specific vaccine.) Of course, as a parent it is your right to determine what enters your child's body, but I believe the anti-vaccine movement has become a public health problem in that those of us who are doing our part to vaccinate our children and help eradicate life threatening and debilitating diseases are being thwarted by those who refuse vaccines and whose children come into contact with ours.
Diseases that were once eradicated in the US are now seeing a resurgence, because a significant segment of the population is no longer vaccinating their children out of fear of vaccines (or even as immigrants from non-eradicated nations.)
My ped discusses each vaccine with me, and lets me know which ones he REALLY thinks are unnecessary. My husband is a physician, and he strongly advocates for vaccination. Whenever our ped mentions the scheduled vaccination, my ultimate deciding factor (after doing our own research) is whether or not his own kids received the particular vaccine. He also lets me know when he believes that seasonal flu shots are really necessary.
I don't believe that anti-vaccine parents should necessarily seek out like-minded physicians, as I believe in having a diversity of opinion and always having a physician who is not just telling you what you'd like to hear, but giving you their best professional opinion.