Funny enough, that was, in part, due to doctors having become a 'gentlemanly' profession in the 19th century! Are you suggesting, SIR, that a gentleman is unclean!?
Class is a funny fucking thing.
Before germ theory, many societies still participated in washing their hands, and some medical texts recommend doing so before surgery. Which, while a less extensive recommendation than in the modern day, is certainly better than the 19th century twits going from autopsies to deliveries without so much as a fuckin' rinse!