Certain gloves are hazardous around rotating members; primarily that leather is far more resistant to tearing than skin. A grinder or end mill will only penetrate a small area and wind up the remainder immediately, taking your appendage along. Even the thin [.002] and easily torn vinyl glove variety are risky.
Stains on fingers and soil under your nails are short term issues: the permanence of missing fingers a bit more. Not to mention possible inability to pursue your avocation.
An old adage, a manager would rather buy hand cleaner than bandages.