I don't wash chickens and also remove the elastic - love the idea that they look uncomfortable!
I always, when I have finished in the kitchen for the evening, put the dishcloths in a sinkful of hot soapy water with bleach in. I am not fanatical about hygiene, but I am very careful about the storage and cooking of food. When I was 16, 50 years ago, my dad almost died from a bug in a pork pie he bought and ate at Woolworths. He was in Monsall isolation hospital (NW GNers may remember this) for almost 5 months and was very seriously ill. When something like this happens to a family member, it does make you more cautious. If in doubt, chuck it out is my motto.