Having your GP on your side is essential. My GP, who also attends to my wife, my mum and other family and friends (all suggested by us as the doctor is so wonderful) was completely supportive. She has said that she has a half-dozen patients transitioning F to M, but that I'm her first M to F patient. A learning curve for both of us. All my health care providers are female, as I feel more at ease around them. In fact, I've rarely if ever seen a man in my GP's practice as she promotes herself as a female-centric practice.
I was willing to walk away from my GP if she showed any hesitancy on helping me transition. Luckily, I live in a very large, liberal city and finding a new doctor would have been relatively easy. I can only imagine how hard it is for people who are rejected by their GP and have no one else in their small town to transfer to. Doctors are human, too. There are going to be some that are not interested in treating trans patients for whatever reason. That's just the way it is, and I wouldn't want to be a patient of someone that doesn't want me there.