People of different races are predisposed to different diseases.
If you see medical care as going beyond just treatment but also inclusive of education and preventative measures, then if you don't factor in race you will be doing a disservice to members of races that are more susceptible to certain diseases.
There are no "members of races", there are different genetic indicators that can be clustered and ordered in different ways. Surely if someone has a (measured) propensity towards a certain disease might have to be tested earlier or treated slightly differently.
A doctor's subjective perception of phenotypical 'race' is not the right diagnostic tool. Questions about ancestors and diseases in the family can very well be, if they are supported by statistical evidence.