9 foods you should not refrigerate. I read the list and there are a few foods that I refrigerate that I may have to change. Butter being one of them. Over the years I’ve gotten into the habit of putting my butter in the fridge, but I remember as a child how my mother always kept butter on the table in a butter dish. Another food is melons, and even though I like to eat them at room temperature, I always refrigerate them. Oh well live and learn I guess. There are seven more foods you should not refrigerate, check out the list below.