1. Mrs. Beasley wouldn’t have anything to do with her new neighbors. She turned up her nose at them when they tried to make friendly conversation.
2. The child was so used to eating fresh vegetables that when I tried to feed him frozen vegetables, he turned up his nose at them and refused to eat.

Compare to: give someone the cold shoulder. Whereas give someone the cold shoulder is limited to people, turn up one’s nose can be applied to people or things.