Yes and no. Shearling is essentially fur, so it's skin + hair. However, since young sheep/lamb is consumed, shearling can be a coproduct of the lamb industry, just like some bovine leather is for beef and veal. Most furry animals (mink, fox, coyote, chinchilla) are either farmed or trapped for their fur. There are some cultures that eat the farmed animals though, but the amount they would eat doesn't come close to the amount of fur that's produced. Basically, shearling is fur, but lambs and sheepling aren't necessarily killed just for their fur.
Winters can get really cold where I live, so I prefer down and real fur to polyester fill and faux fur. Down and real fur is a lot warmer and better at blocking wind, even if the fur is just lining your hood and face. I don't make it my mission to collect down and fur coats. I just make sure to have one, and only one, heavy duty winter coat at a time.
If the ethics regarding shearling are concerning to you, go on google and make your own research and judgement. Try to stay away from biased sites, like PETA.
Personally, I wouldn't get real fur/shearling for anything that isn't supposed to keep me warm, but I wouldn't judge someone or question their morality for having a shearling bag. If you decide shearling is ok with you, get the bag that makes you happy.