“They don’t, they are doctors and I am not it seems to be a matter of class.”
If they have a rule on religious accommodation applicable based on “class”, you will find attorneys offering to represent you for a contingency fee (instead of getting paid, they get a piece of the profits – something they only do if they are sure you will win). You might also induce a heart attack when the employer’s attorney hears about this (a phrase heard often among lawyers: “clients do the dumbest things”).
Make sure the supervisor is aware that this is a request for religious accommodation under the civil rights laws. That will force the supervisor to refer the question to the lawyer. It is also possible the supervisor is unaware of the religious aspect of the beard (many people, especially non-hareidi Jews, are ignorant on this subject).