Unquestioning obedience? Some do, most don't.
However, you have hired the doctor to provide his (or her) medical expertise to keep you or your kids healthy. If you're unwilling to cooperate, you are hampering his ability to do that. If you're not going to let him assist you, I don't see why there's a problem with his focusing his energy on patients who will let him use his judgement to provide the best care that he can.
Note that I said cooperate---this doesn't mean blindly obey his every command. Medical care, especially for children, is something where one should be involved in the decision making. However, not /every/ choice is reasonably up for debate based on your gut instinct. Refusing to see patients who refuse vaccines basically says the doctor considers the vaccination so critical to proper care that if you're not going to cooperate on that, he cannot provide you the standard of care that he is required to provide.
If you have this much of a philosophical difference with your doctor, you don't want to be seeing him anyway, so this isn't a grave injustice. If all the doctors react this way, you might want to consider whether you are the problem.
I don't see any reason to avoid a doctor who behaves like this unless you specifically disagree with vaccination. The doctor is not under an ethical obligation to be a hero to protect every patient who walks in the door, and he may quite reasonably feel that he can do more good by working with cooperative patients than by wasting time with patients who won't let him do his job. If I had an employer who would task me with solving a problem, then discard my solution, I'd be inclined to look for work where my efforts could have more impact as well.