Is it safe for someone who has a bad case of scabies to be cooking at a restaurant? I don't want those bugs!

Scabies. Scabies mites are spread by direct bodily contact with a person, and more unlikely from wearing clothing or sitting on an infected couch. Treating with medication may kill the mite before the rash and itching are gone. Though spread in a restaurant setting is almost impossible, respect your patrons by making sure you are treated and your clothing disinfected before going back to work.
Creepy...but... Unless the chief is wrestling semi clothed with the patrons they have no risk of catching scabies.