1. John said he planned to wear shorts and a sweatshirt to the wedding, but I told him it would be completely inappropriate. I told him he would stick out like a sore thumb and everyone would notice him.
2. The paintings of the modern artists stuck out like a sore thumb in the classical art museum. They just didn’t belong there, grouped together with the old masters.

Compare to: stand out in a crowd. Whereas stand out in a crowd is usually a positive attribute, stick out like a sore thumb is a negative one. It is used to describe someone (or, less frequently, something) in a situation where one ought to blend in but doesn’t.