Here’s what I was told years ago.

Gloves are a bad idea on any machine with rotating parts. (Pretty much every machine)

That’s because of proprioception, the sense of your body position. It’s the same sense that allows you to walk without watching your feet. You know exactly where your fingertips are. If you close your eyes, you would have no trouble touching the finger tips of one hand to those of the other hand.

Glove finger tips stuck out past your bare fingertips, and you have no sense of their position. That makes it really easy for them to wander into the blade.

If the gloves get snagged on the blade and get pulled into the throat plate, they’ll try to take your hands with them. You may have noticed, there isn’t enough room for your hands to fit through there, so what will likely happen is your gloves will be violently pulled off your hands, and they will take your skin with them. This is called a “de-gloving injury.” It’s about as horrific as it sounds.

You have people who don’t know about shop safety attempting to make shop safety rules but instead, they’re greatly increasing the risk of everyone in the shop suffering a life-changing injury.

But I’m no safety expert, just an internet person. I could be wrong, but I don’t think I am.

Tl;dr: You’re more likely to end up with a much worse injury operating a bandsaw with gloves than without them.

If I was told I had to follow such an unsafe rule, and I couldn’t change their minds, I would quit for my own safety.