Which takes precedence: the female disbeliever doctor or the male Muslim doctor, in the case of a woman?

Question:
This is also a letter we received from the wife of a Muslim doctor, in which she asks: Which is better: the male Muslim doctor or the female non-Muslim doctor? I mean: for examining women.

Answer:
If a Muslim female doctor is not available, the female disbeliever doctor is preferable to the male doctor regarding the exposure of women's private parts, and it is safer. In my view—and Allah knows best—the female disbeliever doctor who is trustworthy, from whom no harm is apparent toward the Muslims, and who shows sincerity to the Muslims in her medical practice, is preferable to the male doctor in treating women when there is a need for it.
However, if a Muslim female doctor is found, she suffices in place of the female disbeliever doctor. Then comes the Muslim male doctor, followed by the disbeliever male doctor, in this order: first the Muslim female doctor, then the female disbeliever doctor—for women, I mean—then the Muslim male doctor, then the disbeliever male doctor when there is a need.
Whenever it is possible to do without the disbeliever male doctor and the female disbeliever doctor, it is preferable to rely on Muslim male doctors and Muslim female doctors. But when there is a need, and the Muslim doctors and female doctors are not sufficient, there is no harm in using the disbeliever male doctor and the female disbeliever doctor when there is a need for them, provided that care is taken to ensure they do not display anything that harms the Muslims, or call the Muslims to what harms them, meaning by some of the rituals of their disbelief and misguidance. They should be occupied with their task, not using what harms the Muslims in their calling to falsehood, or teaching falsehood, or the like of that which harms the Muslims.