I can choose to do business only with left handed redheads with green eyes if I wish. Or not do business with left handed redheads with green eyes if I wish.
There might be exceptions for life or death situations but other then that my right to choose who I do business with should be inviolable.
Once more you fall on your statement of a civil right.
I speak of rightness on a deeper level. Perhaps by access, the more conscientious physician could do more good than one who was more laissez-faire about homosexuality.
On the other hand as I have also surmised, the doctor could have felt inadequate.
The kind of jobs you do are not on the level of the practice of medicine. They just aren’t.