The NP covered this issue back in 2013

http://nationalpost.com/news/canada/patients-shouldnt-be-allowed-to-choose-doctor-based-on-race-gender-medical-group-says/wcm/21ccd8b4-3ed1-4f57-89c8-b1b57d591db5

"Physicians say patients, even in emergency departments, sometimes ask for a doctor or nurse of their own sex or ethnic background"

"Some doctors, however, say accommodating such a preference when it is based on a new immigrant’s deeply rooted cultural background can actually lead to better health care, and call the Society’s position overly rigid."

"In her immigrant-focused practice, Dr. Nitti said female patients frequently request a woman doctor because of their cultural or religious background, or past experiences. Alternatively, a patient might say “I would like to see a Southeast Asian provider.”"

So I guess it is ok to ask for a doctor of a particular race, as long as the word "white" is not involved.