Until a few years ago, if my physician was educated in the United States and were Asian American they had to have a measurably better academic track record to overcome anti-Asian bias in university admissions. Does that mean they are a better physician? Probably not - in my experience the difference between good and bad in a medical context is patience and care, not knowledge. However it’s not absurd to make the opposite claim.

Similarly, there is a body of scholarship that suggests that black physicians trust black patients more than white physicians trust black patients. If I am black, does the color of my physician matter when I talk about something hurting? The evidence suggests that it might.

The fundamental flaw in basing your moral philosophy in measurable metrics is that metrics are noisy and that noise will often undermine your point. Instead, you should be making a purely moral point: my doctor’s skin color shouldn't matter and I will act to make the world I live in more similar to this ideal. That moral point is the driving force behind the civil rights progress that has been made.

(EDIT: I had not read thoroughly your comment, see my PS below for a direct reply.)

Your point is to use a proxy for the variable that really matters.

Unfortunately that proxy is neither reliable, nor has good impact on the society in general.

It is better to just use the pertinent variables directly without a proxy.

Your physician is good if e.g. they have also a research formation, if their patients are satisfied and have a good recovering rate for illnesses that promise recovery, etc.

PS: ok, I see that you also point to variable trust from the patient to the physician based on superficial criteria. I hope that can change in the near future when everybody has the mindset "the appearance is not what matters". The patients themselves will benefit from growing their openmindedness.