Be careful not to generalise feminists. The actual, genuine, dictionary definition of a feminist extends to a lot of good, sensible people (myself included) and the general image of militancy or hatred that is often associated with the term is thoroughly unwarranted.
What you'll probably find is that the people you describe consist of a tiny proportion of the general population, or even of the feminist movement. Female sexists do exist, and should be treated as any other stubbornly ignorant group (racists, militants, etc.) - in my experience, people of that kind will not listen to reason and are best ignored.
I would, however, argue that referring to doctors and nurses as specific sexes IS somewhat insensitive.