Most people have experience wearing gloves to protect their hands. You probably do too. Maybe you wore them while you were working in your lab or while you changed the oil in your car or last night when you washed the dishes. You made some decisions when you wore those gloves. You know oven mitts aren't good for changing oil, and leather work gloves wouldn't have been too helpful when you did the dishes.
Nitrile gloves work for the former, butyl gloves for the latter.
Switch the two and you've got contaminated hands. There are different kinds of safety glasses, different kinds of goggles, even different kinds of lab protective clothing. PPE should be your last choice for protection. Train employees and students to know when to use their PPE, its limitations, any special techniques for putting it on and taking it off, how to take care of it, and how to get it. Documenting doesn't have to be a bunch of new paperwork for this.