Personally I couldn't care less what my doctor's political or religious beliefs are, or his age or much of anything else other than him being skilled and my insurance will cover most of his fees.
The guy's personality plays into it a little but only because it could influence his suggested course of action (eg if he's arrogant, he might not consider that his initial analysis was wrong), but that aside, how good he is at diagnosis, treatment etc is about 99% of it for me. This is a doctor I need, not a date.