no they dont
Assuming you mean why "Most" butter must be refrigerated. I believe the answer very simple. Butter is not solid at room temperature. People usually prefer to spread their butter rather then pour their butter (except in the case of pop corn) so it is *Recommended* that is Refrigerated.
Yes.
coconut body wash and coconut body butter
yes
The fats in butter become solid and firm when refrigerated.
Peanut butter has a natural preservative in it. It does not need to be refrigerated. It will keep for months out of the refrigerator. How about "natural" peanut butter? I read that there is a cancer-causing mold in peanut butter, and if left un-refrigerated, can grow?
If it is an egg custard, it should be refrigerated.
Cheese is refrigerated.
coconut oil
Many of the common uses for coconut butter are for enjoying with a meal. The most common uses are as a spread, over food as a butter alternative, and as an ingredient in many food items.
From a food safety standpoint, butter is considered shelf stable. But you get longer life out of it if it is kept refrigerated.