Mostly religious, but it was customary even for the non-religious. It is generally thought to be better when performed by surgeons (or wannabe surgeons in the case of medical students) and even non-surgical MD's (I am not a surgeon) rather than amateurs with not-very-sharp scalpels and not-quite-sterile technique.
Why would I regret? These people would be doing it without medical doctors supervising if there wasn't a regular medical mission servicing remote areas.