I'm not sure. Virtually everybody in the US was immunized with the MMR vaccine (at least those below a certain age...which is perhaps in the 60s, by now), so that one may be kind of automatic. The military requires a series of vaccinations, and that gets to the bigger point. I don't see any federal requirements on mandatory vaccinations, not for MMR (measles, mumps and rubella) or COVID. Vaccine mandates tend to happen at the business level. A doctor in private practice can probably do whatever they want, but a doctor working in a hospital probably cannot, and since virtually every doctor would probably start out working in a hospital, there may be a de facto mandate without a true mandate.

That's how COVID mandates are going, as well. It's employers making the decision, not state or federal governments.