Sorry, it's only pediatricians. They specialize in children. Most general practitioners won't see children because they're not set up for it.
And the reason why pediatricians aren't that understanding about parents not choosing to vaccinate is that it puts all the other children in danger. Your perfectly healthy child may be able to go through Mumps, Measles, Chicken Pox without being hurt (maybe -- measles can kill), but exposing a child with cancer to that could be fatal to the other child. The pediatrician isn't going to risk the health of hundreds of other children to risk that.
Also, parents who choose not to vaccinate are notoriously difficult to deal with. They tend to have an education made up of whatever they read on the internet, and they aren't always able to weigh risk versus reward. So, that's why it's hard to find a pediatrician who will understand your desire to not vaccinate.
BTW, if you do find a doctor who doesn't care if your child is vaccinated, please understand that your child can be exposed to whooping cough and other fatal diseases when you bring your child to the office. It would be terrific if your child's one-year checkup or "just a cold" turned into a fatal condition because you chose a doctor who didn't require patients to get vaccinated.