Are you referring to a broody hen pooping on the eggs she's incubating? It didn't sound like you meant eggs for eating or selling, but am I mistaken?
If you're talking about a broody, I'd wash them, then take her off the nest once a day and put her in front of the food and water. Some broodies need a brief training period, they usually catch on after a few days of being taken off the nest for a break.
There are those who say never wash hatching eggs, but I do it often, and they still hatch. The bacteria and digestive enzymes are a bigger threat to the embryo than being washed. The "bloom" gets rubbed off by the hen's belly anyway. A little soap and water is really not a problem. You should see what commercial hatcheries do to them, and they still hatch.