My (short) experience working in health care suggest both are very bad qualifications for a health professional.
I'm curious, though, why you would not want someone who was genetically smart? Why would you want a "dumb" healthcare professional treating you? Do you not believe intelligence to be related to genetics?
Also, how does being male make one a worse healthcare professional?
If you are saying you want fairness in opportunities, then isn't discriminating on the basis of someone being male the opposite of fairness?
An exception is if you may need the doctor to insert a hand into your body. In this case, note that Asian female doctors generally have the smallest hands.
An exception is if you are very heavy and might require feats of strength for your care. In this case, young non-Asian males are most likely to have the needed strength.
I would actually say no, at least when it comes to when arguments for a meritocracy are used as arguments against redistribution of wealth from the more "meritocratic" to the less.
Consider, as a thought experiment, if instead of features like intelligence, communication skills, self-confidence, etc., that our economic system instead only valued basketball skills as the means for distributing wealth. That system would be a meritocracy: great basketball players with tons of talent and effort would be really wealthy and successful, while talentless or lazy basketball players would be poor.
I think this is a good thought experiment because of some of the things it highlights. Perhaps most importantly, all short people are pretty much destined to be forever poor in this meritocratic system. If you are short, what value would you see in abiding by this system at all if tall, great basketball players took all the gains? What about if instead great basketball players could be wealthy and successful, but they still had to pay a very large amount of taxes to ensure that short people didn't starve (or revolt).
While a (true) meritocracy may be ideal for how jobs are to be distributed, if it is also how wealth is distributed it means that it is also, by and large, a lottery of DNA. How is that any more "fair" than an aristocracy?