I’m in the “no way in hell” camp. By the time those hands have finished washing the dishes, the hands (and the dishes) are no longer germs, as the warm water and soap have removed the pathogens. If continuous sneezing and coughing are happening on the dishes right after they are washed, and they are used again right away, then maybe, but not from the hands. And really, if someone has the actual flu, don’t let them be standing and washing dishes, they are too sick to be doing that. Lend a hand, do the dishes for them.