A doctor can refuse to see you if you don't have insurance or your coverage isn't accepted. However, they will see you if you have the ability to pay for the services. In contrast, if you present to an emergency room, laws provide that you will be seen and treated by a physician for your injuries or ailments.
No doctor should refuse to see you. But you will have to pay the bill when it comes due. Why not go to a doctor that takes your insurance. He can only refuse to see you, if you were a patient and over time you were uncooperative.
Sadly, yes he can. If you have Medicare it's worse. Only certain hospitals take it. Try a State funded clinic if you have Medicare, they take that insurance.