Hi all,
Just adding my experience to this list. I bought a 2015 rMBP in late January 2016. Immediately started having crazy peeling of the skin on my fingertips across all ten fingers. They would peel, then crack, and become red and very painful as several layers of skin peeled off. It basically looked like I had no fingerprints.
I didn't initially suspect the rMBP was the cause, so I went to several doctors and dermatologists, and finally the derm gave me a shot of cortisone, which immediately stopped the peeling. Apparently he said this kind of peeling can be hard to stop once it starts because daily activity puts a lot of stress on your hands, so hard to rest them to heal fully, and the cortisone shot helps cut the inflammation. He suspected it was the laptop given that it affects all ten of my fingertips but no other part of my body, and so I returned the laptop, thinking maybe there was some random chemical that got on the keyboard during production, because I've had a 2013 MBA for years without problem. Bought a different rMBP, and the problem immediately returned. I've now returned that one and am waiting for the peeling to go away (it seems to take a week or two to stop).
Unlike everyone else, I suspect it was the keyboard rather than the trackpad, as it's across all of my fingertips, and I don't use the trackpad with both hands, only the right one. I also never use my pinky finger with the trackpad, but it's on all fingers. My doctor also thought it was the keyboard, as it's the only thing I touch with all ten fingertips but no other part of my hand/skin.
I called Apple and their engineering team looked into this. I thought perhaps I had an allergy to the paint on the keyboard of some component on the keyboard, but they weren't able to be specific about what chemicals comprise the keys or the paint, so I wasn't able to narrow it down. I'm planning to do patch testing with a contact dermatology specialist in the next few weeks to see if I am allergic to any common chemicals used in laptops, but otherwise am at a complete loss as to the cause of this problem. I'll report back if there seems to be any connection between an allergy to a chemical that might be used in the laptop.
In the mean time, I'm not sure what to do. I'd love to remain a Mac user, but I don't want to play finger peeling roulette any longer! I may just give up a get a PC...