I figured they were more diverse before they started conquering other species. Military service seems to be pretty strongly associated with the nobility. My guess is that when they got some other worlds and species under their control Klingons as a whole became quasi-nobility and other species started filling menial jobs. This probably came to a head around the time of ENT. Some jobs, like lawyers and scientists, are probably restricted to Klingons for security reasons, but not as well respected since they’re not traditional professions for nobles.