I have seen very ugly toe nail injuries from open toe sandals on the river and always keep my own piggies covered with Keen type sandals or river shoes but that is for my own safety not that of the boat.
Those would be some scary toe nails. The dog has badger claws and ive never seen a scratch from her tearing around the tubes trying to get at the fish I'm landing. Not that Ive seen everything but ive never had a boat in the shop with a customer claiming toenail rip.
I have torn the hell out of my toenails many times but still havent learned my lesson. Peeled one back the other day flipping a boat over in the shop. Rubbing strake snagged me. Some day i'll buy some shoes.
If your raft can't take toe nails then I would be very worried about going over rocks. My family and I always have open toe shoes as does my dog and none have ever made a scratch in the rubber. Sounds like a loon.
May the wind be always at your back,
May the sun shine warm upon your face.