One does not wash one's dirty linen in public proverbial saying, early 19th century; meaning that discreditable matters should be dealt with privately. The French saying ‘c'est en famille, ce n'est pas en publique, qu'on lave son linge sale [one washes one's dirty linen amongst the family, not in public]’ is attributed to Napoleon.
wash one's hands of disclaim responsibility for; the original allusion is to the biblical story of Pontius Pilate who, when he was forced to condemn Jesus, sent for a bowl of water and ritually washed his hands as a sign that he was inncoent of ‘this just person’ (Matthew 27:24). In proverbial usage, the attempt at avoiding guilt is often seen as futile.
See also one hand washes the other.