I soaked white beans for 4 hours, shall I pull the peelings off that are separating from the beans, or cook the peeling as well?
You certainly can leave the skins in - but you don't have to.
The only reasons to pick them out would be if you don't like the appearance, or if the dish leads to loose skins that you find unpleasant.
I soak overnight before slow-cooking, and don't deliberately remove skins, but some come off in rinsing and are left behind. At the start of cooking, many beans still have their skins on, which then go on to fall off as they're cooked. This means that to avoid loose skins in the finished dish you're likely to have to put some effort in to removing them all