Hands, finger and loose clothing don't belong anywhere near rotating bits or anything that cuts while its in motion. Gloves or no gloves.
I also make sure I am not in line or in front of the cutting surface.
These two simple rules have gotten me through my 50 years of life with all my digits and no injuries to speak of over a career of working on, around and in machinery.
And yup, I wear gloves pretty much everywhere. Mechanix gloves all around the shop and a rubber/latex coated fabric glove (pretty much like a layer of skin) around the lathe.
It's not about the gloves, its about keeping your mind on the task at hand. Reaching in to a work area with your hand to grab a chip or curl is bad practice no matter how you slice it. Slice it is the key word here.
I'm almost always wearing ear defenders around anything that makes more than conversation type noise (a lifetime around jet engines and bad tinitus as a result will do that to you) and eye glasses go on (and come off) at the shop door. Rings, watches, etc are things I don't wear, just something I picked up when I started in aerospace soo long ago. Not even my wedding band.
Lots will disagree wih the way i look at it. So be it.
SA is king as far as I'm concerned. If you stay aware, you stay alive. That's the way it is at my work and my shop at least.