Given a choice, I tend to select female physicians over male, but that's because I find it is easier for me to be honest with them about problems. With a male physician, I really tone things down; minimize even more than my usual level, and unless I know them very well I tend to just agree with what they want to do even if I think they are wrong. "Whatever you say, just get me out of this exam room".
It's not them, it's me. I think I have some old DNA that makes it harder to admit to medical problems to a man; my theory is that I am worried it will lower my status in the herd and therefore my mating fitness.
Yeah, that's mainly a joke. Mainly.
A second possible factor was that my first pediatrician was female and tried to take good care of me, though she was way too old in the days before CME. I changed to another pediatrician--a man--who was a jerk with me. Then in college I saw female NPs in Student Health who listened, except one male NP who did not. And then a male GI who did not listen followed by a female who did. It just worked out that way.
But, I've also gotten into trouble by selecting females over males at times with no good reason. Years ago a female PCP was suggested by my (male) colorectal surgeon. She was a good doctor, I liked her a lot. We worked very well together unlike my previous (male) PCP, though the trouble was more with his office staff than he. She monitored my health while I was very sick and on some dangerous meds. I could talk to her one scientist to another and agree to overrule her staff. Sadly, she moved out of state.
BUT, when she sent me to other MDs, they tended to be female, and some of them turned out to be kooks. They were all working at the same hospital, which was very male-MD-dominated, so they tended to band together. I can understand that, but fact that there were few female MDs allowed for the recommendation of physicians who normally might not have been on the top referral list. 'Cause they were the only ones she worked with. (My PCP did warn me that one of them was a bit odd--incorporating things like aromatherapy--but an allergist that she thought was great turned to be nothing than one of those assembly-line shot-factories who had no interest in dealing with my immune system problems (which is why I had been referred), just interested in doing skin tests and giving me allergy shots. The whole office could only talk tests and shots; it reminded me a LOT of my orthodontist as a kid.
I also happen to know from my years in medicine that there is a certain percentage of female physicians who should have been flunked out but people were afraid to because they were female. I worked with two residents, one who seemed smart and another who was darling but clearly an idiot. The one who appeared smart did constantly stupid things; I don't know what happened to her but I think she was helped to finish her residency somewhere else. The idiot went to work for a large second-rate HMO. I would be afraid to let either one touch me.
In some medical schools with a low female census, women may get passed who should not. The professors are afraid of flunking out the only woman in the class so they bend the rules, or convince themselves that there was some sort of gender-based bias. I know how this can happen, as I did it as an instructor myself in another scientific field. There was a young woman who was very bright and cute and did not seem to do any of her own work; she had a line of male students following her around with their tongues hanging out. I thought she was just busy, I did not realize she had basically done none of her work all through school. She certainly had the brains and ability, she just never needed to learn anything. I did not realize it until I had to work with her years later.
I made the same mistake for a male student who was a quad in a wheelchair; I had seen him come through the ER the day he had the accident as a teenager but he did not remember me eight years later. I took pity on him and assumed his faults were the fault of communication problems due to the injury, when in reality he just was not qualified.
This is not limited to female or handicapped students; you see it in "Doctor Dynasties" as well. You can't flunk the kid who is the grandson of the man who founded the anesthesiology department, you see. But in areas where one gender or one-whatever is under-represented, a certain % who should not make it through, will. And that is a massive disservice to all their classmates of that same status who are very competent and are made to look bad by that one fool. Twelve female physicians graduate and 11 have worked really hard, while one is incompetent.
That's my $0.02 on choosing doctors by gender. If you are a bit messed up in the communication-department like me, it is probably with the risk on making gender a reason for selection, but if it is a female in a female-limited filed, you run a risk of some chaff in with the wheat.