My wife, Lenore, doesn't believe in vaccinations. I do.
We have a simple way of resolving conflicts like this. It's the "Who Feels More Strongly" protocol. We discuss it until it becomes clear which of us cares the most. Then that person gets her way. Or his way. Or her way. Or his... This protocol works well because it's self-correcting. If I were to feel annoyed that "she always gets her way" then I would start feeling stronger about getting my way... and then I would get my way. In practice that isn't a problem.
Lenore felt more strongly against vaccinations than I felt in favor. So, we didn't vaccinate Oliver. Meanwhile, I did find a justification that made it easier for me to go along: Vaccination is but one of a spectrum of ways that we protect the health of our child. We live in a relatively hygenic environment (arguably too hygenic, if anything), Oliver nursed on healthy breast milk until 20 months, we can afford health care, etc.
Then one day we went to the doctor. Oliver had what seemed to be Strep, and while there I figured I'd get a flu shot. Lenore always has me go with her to the doctor-- I'm the bodyguard; her personal lawyer.
The doctor asked if Oliver had his shots.
"Nope." I replied.
The doctor began to explain that vaccinations are very important. I cut him off.
"I'm sorry doctor, but values are, as you know, trans-scientific. That means science can't answer questions about what risks are worth taking. The weighing of risks is not primarily a rational issue. It's a personal and social matter."
"But wait a minute," he glanced at his paperwork, "YOU are here to GET a vaccination!"
"Oh yes. I want a flu shot."
"That doesn't make sense."
"Sure it does, Doc. You see, I personally believe vaccinations are important and helpful. I believe that the risks are probably minimal. Therefore I want my shots. But I'm also standing here as a spokesman for my family. Speaking in that capacity, our position is that Oliver will not be vaccinated unless and until he decides he wants it. He doesn't want it, so we don't want it."
(Strangely enough, I became pretty sick about a week later, with flu-like symptoms. I decided not to get flu shots after that.)
Moral of the story: Lenore and I find ways to work through our different parenting beliefs and support each other.