Never, never, never on rotating machinery unless, say, you are the helper taking cut stock off the outfeed of a tablesaw or planer and never near the blade.
Same for drills, wood and metal lathes, routers, etc, etc.
It's the risk of being snagged and losing more than a finger.
Leather gloves for wire brushing or angle grinding as you need something and they're less likely to snag like a fabric glove.
If you have a sensitivity to something, then PR88 barrier cream and or disposable nitrile gloves that will rip.
All that said, I like v tight fitting knitted kevlar cut resistant gloves for those handling tasks where you need some protection. Shifting metal and timber stock about.
"Hands - fingers - wrists" was a campaign at work (FTSE100 engineering co) for a few years. These account for a significant proportion of industrial injuries. Proper methods with proper tools helps a lot. Broadly, PPE is there as the last defense when something else has gone wrong.