You asked, "what would you do?"
So I'm going to answer for me.
If I were in your position, I'd do nothing--it would be my coworker's role to do anything.
If I were your coworker, I'd just get out the Lysol wipes. Or not.
I personally am not that grossed out by bare feet. I'd be more worried, actually, about hands w/ cold germs on them, or food, or other stuff. I touch my own bare feet sometimes, and I don't go wash my hands.
I guess there's the possibility of warts, but even that is not terribly likely. If I were worried about it, I'd use Lysol wipes. Personally, I'm not that worried about it.
I'd view the psychological gross-out factor as the biggest one, and since I'm not grossed out, I wouldn't bother.
However, if your coworker is grossed out, I think that's perfectly legitimate, even if there weren't a company policy. And I'd say he could completely go to the supervisor and ask that something be done.