I worked at an independent shop, it was 2002 and one of the owners started having serious skin issues, he told us one day we were going to start using gloves, which were provided. It seemed odd at first but I quickly got used to it. I honestly think that a lot of his issues were to using the parts washer without glove, which I always used the gloves for, but the years of grease gasoline and oil didn't help him.
I have wore gloves ever since.