I think you are confusing cleanliness of the mind (which incidentally may be different gor people of different faiths or no faith) with hygiene.
Why wash hands over a dead animal, why not after one had handled the animal?
Washing feet is ritual, what about hands etc.
Not going further...
I think you have in mind the ceremonious ritual of the Pharisees - Mark 7:2-5; Matthew 15:2 __________
David too spoke about washing his hands at Psalms 26:6 in the sense of being morally clean.
Water was used at Deuteronomy 21:6.
Water for hygiene was used at Leviticus 15:5-12 see also...