Nitrile gloves. All the time. Every time.
Used oil is carcinogenic, as well as being difficult to get out from under my nails, so I prefer to minimize the exposure.
Nearly every day that I am home, my hands are in some woodworking finish, gun solvent, automotive fluid (clean or dirty) and none of that stuff is good for you with chronic exposure. I'm not about to give up my hobbies or interests, so nitrile it is...