I discuss this decision with families even before a child is born. I tell them it's important to pick a pediatrician who shares their beliefs, as the doctor-patient relationship is a long one in pediatrics (hopefully cradle to college). Even if there may be some other disagreements down the road, you need to begin the relationship on common ground.
I've practiced long enough to remember doing spinal taps in my office and treating children with meningitis or bacterial sepsis. There were long nights spent in the ICU with families, and unfortunately, a few patients died. Some are now deaf or have other residual effects of their diseases. Each case was devastating, and I'm sure the families of every child who perished would have given anything to have a meningitis vaccine or a chickenpox vaccine for their youngster.
I understand that all parents have to make their own decisions for their children. At the same time, I get to choose how I practice pediatrics. That being said, my parents choose to vaccinate their children and we happily start off the parent/doctor partnership together. I also sleep better at night not worrying that their children will contract a vaccine-preventable disease.