While we are washed in the blood and cleansed as we are infused with righteousness in our growth towards sanctification, the righteousness of Christ is imputed. It’s an extrinsic covering like when Adam and Eve sinned and God sacrificed the animals and clothed them with the skin of the animals. It’s a covering or a clothing in a robe of righteousness:
I will greatly rejoice in the LORD; my soul shall exult in my God, for he has clothed me with the garments of salvation; he has covered me with the robe of righteousness, as a bridegroom decks himself like a priest with a beautiful headdress, and as a bride adorns herself with her jewels. ~~ Isaiah 61:10
"Blessed are those who wash their robes, that they may have the right to the tree of life and may go through the gates into the city. ~~ Revelation 22:14
By virtue of His relationship with humanity our sins can be imputed to Christ. In His incarnation and baptism He comes into union and solidarity with humanity. He becomes the Son of Man and therefore, our representative and proxy before God so that He dies for our sins as our representative and proxy. We die with Christ as He identifies Himself with us. By faith we enter into mystical union and become one with Christ as His righteousness is imputed. We are crucified with Christ as we are baptized into His death and risen to new life. Just as those who enter the lake of fire are baptized in the lake as they die to the old self (ego death) and risen to new life.