I wear contacts, and my instructor just has contact lens-wearing students keep their eyes closed. He taps them on the shoulder to let them know when the mask is half full for that part of the mask skill exercises.
Besides, not everyone loves the feeling of chlorine or salt in the eyes. I'd rather keep my eyes shut unless it's an emergency situation. And if that's the case, I'll have a lot more to worry about than losing a contact lens or minor stinging. I'll be fine with that.
When I go on dive trips, I make sure I have spare lenses, backup glasses, and contact cleaner supplies handy in my luggage (the cleaning supplies go in my checked luggage so I can avoid the hassle of pulling it out while going through security)
Once, a number of years ago, I dove into a swimming pool and rinsed a lens out and spent a weekend without one lens. I'm not eager to repeat that.