I've snorkeled with contacts, and scuba dove with contacts, down as far as 70 feet or so. I got a little water in my mask on the deep dives, but it usually leaks in a little around my beard/moustache. It really isn't a problem since you are usually face down anyways, so the water just lays on the glass, or pools around the bottom if you look forward. You really have to flood you mask or splash it around to even get it in your eyes, and if you do, it shouldn't bother you all that much. I've had contacts for years, so getting stuff in my eyes doesn't bother me as much as most people.
If you have sensitive eyes to begin with, , it may bother you, but you're more likely to get red eyes from the water and sand at the beach than through a properly fitted mask.