Who does the triune God wash according to this passage?
The triune God washes sinful men—people like the Corinthians—and those who were no different. Though they may not have been steeped in idolatry or gross immorality, the potential was there; their hearts were born wicked. Through grace, the finished work of the cross, and faith in it, they are washed, sanctified, and justified.
Les explains that this passage shows the working of all three persons of the Godhead: God the Father in heaven looks down on sinful men, the Holy Spirit convicts sinful men of the finished work of God the Son, and the whole triune God comes in and washes these kind of people of which you and I were no different. He notes that though we may not have been steeped in idolatry or practicing gross immorality, the potential was there; his heart was born just as wicked as these Corinthians, and so was yours. As a result of the grace of God, the finished work of the cross, and our faith in it, we too have been washed, sanctified, and justified.
And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God.