I make homemade ice cream and it can help to have the ingredients cold to begin with so you don’t have to chill the base before you churn it. But there’s not enough vanilla extract in ice cream (or probably anything) to even make a temperature difference so idk why anyone would refrigerate it.
The original patent for peanut butter (literally called peanut-candy) specified the peanut paste is mixed with sugar. So Jif is legitimate peanut butter even though you want to be snarky about its sugar content.