I don't use gloves. I see why someone might want to, but you can't wash them (also, that would defeat the purpose) and it seems wasteful to me to throw gloves away. I don't normally use a lot of "anti" cleansers, but I definitely use hand sanitizer after bum changes.
I usuallly only have issues with my hands cracking right by my nails on the tip of my fingers. I put a dab of polysporin on, with a bandaid for half a day or so.