If you don't refrigerate Uncrustables, the preservatives used in them will start to break down and cause the bread to become stale. This also increases the risk of bacteria growth as bacteria can take hold on food high in sugar or carbohydrates that have been left out too long - such as an uncrustable sandwich.
Not only should you keep your Uncrustables stored at a safe temperature, but it's important to follow the other storage instructions on their packaging, such as not exposing them to direct sunlight or heat and consuming within 24 hours after opening. Eating expired Uncrustables will increase your chance of adverse side effects like diarrhea, nausea, vomiting and abdominal cramps. So make sure you store your Uncrustables safely by keeping them refrigerated!