This thread came to my mind while playing my game today. In my current family the mother is a vampire and she has awful reputation, near atrocious. She has gained it by drinking from sims and being seen. The father is a spellcaster with a Curse of Unwarranted Hostility which means other sims will randomly attack him - his reputation is atrocious. While both of these sims are supernatural, their reputation has gone bad without me purposefully trying to make it bad. So bad reputation is definitely a thing that can happen although it may not be very common.