The AMA is, in fact, a 501-c. It also, in fact, does not prosecute licensure issues. It does, in fact, hold de factor control over every medical licensure board in the United States. If the AMA supports an action against a doctor, it is a foregone conclusion that the doctor will lose their license.The AMA is a 501-c lobbying group like the NRA. They have no statutory power over medical licensure. Medical licenses are run by the state per the state Practice Act, not the AMA.
That being said, the only valid medical exemption is probably an allergic reaction to the 1st vaccine. Anaphylactic reaction would certainly be a legit medical exemption. I do agree any medical exemptions would be rare for this type of vaccine. Religious exemption may be an easier route, legally.