A lot of people think it's wrong to wear animal fur, and a sheep skin coat is in the same category because it is made of an animal's skin. People can wear fabrics that come from plants, like cotton or flax. Wool is also acceptable, because no animals die when it is gathered.
If I buy one of the fantastic used sheepskin coats from ebay (as i did) then the animal on mine was killed in 1975, I cant turn the clock back and I think to say burn it, would be sacrilege to the memory of the sheep, a waste of what nature gave us to use. I live in a remote part of Scotland with a smallholding when we slaughter the animals for our meat we always sell the skins to a coat maker, why would you waste it? Crazy. I have my 70s knee length sheepskin with a waterproof smock I have survived temperatures -20 windchill layered up. Sheepskin is the ultimate fabric, warm when my other wool coats give up, windproof. OK heavy. Why don't I buy an expensive down jacket? I cant afford it from crofting. Oh, and don't need one since I got the sheepskin.
No, there isn't anything wrong with wearing an old sheepskin coat. Sheep are not an endangered species. If that was the case, then the ethics of wearing coats made of their skin would be much more questionable. Additionally, people already wear articles of clothing made from wool, yet no one seems to call into question the ethics of shearing sheep for their woool.