As a general rule of thumb, condiments containing dairy, vegetables and fruits need to be refrigerated; those containing vinegar, sugar, salt, and alcohol probably don't (but may benefit from a stint in the cold).
Do you have to keep condiments in the fridge?
“Condiments that must be refrigerated after opening have specific characteristics that make them more susceptible to bacterial growth when they're left out at room temperature,” said Katie Heil, a certified professional in food safety and senior editor at StateFoodSafety.
Do ketchup and mustard need to be refrigerated?
Answer: Technically speaking, you don't have to store opened bottles of ketchup and mustard in the refrigerator. ... An opened bottle of ketchup should stay at peak quality for about 9 to 12 months in the fridge; mustard for at least a year.