At least I would hope they can.
Lawyers, CPAs, and other professionals can pick and choose their clients as they see fit -- without revealing the reasons to anyone. Why not doctors?
Now... if these same professionals work for a company or organization that serves the public at-large -- then discrimination may become obvious. Like refusing to do business with or treat Muslims, for example.
It would be best for professionals with strongly held religious, political, or racial opinions to go into private practice.
>> It would be best for professionals with strongly held religious, political, or racial opinions to go into private practice.
Of course, Hillary-care could make the a difficult option.