A doctor is there to save your life. And btw, I personally try to get female docs, as much as possible, though in some fields, that is more difficult than others.
Hairdressers OTOH, are not a necessity of life, but a nice luxury. You can always chop off your own hair, but you cannot take out your own appendix. I would not go to male Jewish hairdresser, there are so many females in the field, there is no justification for doing so.