I have never heard of using pits and skins to make anything. Peach butter sounds really good. I wonder if the same could be done with mangos since HEB has ripe mangos right now.
I wouldn’t use mango skins. Mangos are cousins to poison ivy and the poison is in the skin. I found out the hard way. But any other fruit like apples and plums would be fine. Don’t use apricot pits because they have a poisonous substance inside but the skins are fine (most fruit pits/seeds have various levels of this substance but apricot is at the top of the list, ymmv).
Anyway, there is lots of fruit pulp and juice in the skins and pits/seeds after peeling so why waste it? Put all that in a pot with some water to get it going and cook it a while to get it mushy. Dump it into a colander or cheese cloth and let it drip into a bowl/pot for several hours. The clear juice won’t be as crystal clear as jelly made from the meat of the fruit but still clear enough for jelly. Then, discard the pits/seeds and mush the skins around the colander (aluminum sieve with pestle). This will give you the pulp to use for butter. Discard the used up skins. Use the same recipe for the butter as you used for the jelly except add some cinnamon, nutmeg and/or allspice.