"Even when we do our best, our righteousness is filthy rags in God’s sight (Isaiah 64:6). Do you agree?"
No, I do not. Works-salvation is rightly rejected by scripture, but so is dead faith. The religious acts Isaiah is describing are filthy not because humans always fail—though that is also true—but because there is no real relationship with God. Let’s look at the passage in context:
5 You come to the help of those who gladly do right, who remember your ways. But when we continued to sin against them, you were angry. How then can we be saved? 6 All of us have become like one who is unclean, and all our righteous acts are like filthy rags; we all shrivel up like a leaf, and like the wind our sins sweep us away. 7 No one calls on your name or strives to lay hold of you; for you have hidden your face from us and have given us over to our sins.
The prophet Isaiah paints a vivid picture of the apostasy of the people of God, from 1:2 all the way to the final section of the book. Apostasy is why they are clad in "filthy rags," not because their best isn’t good enough. Filthy rags may be equated with insincere religion, hollow faith, and hypocritical attempts to manipulate God.
Israel had forgotten the Lord. They lived in sin, without any intention of pursuing holiness. So worldly had they become that God had “given them over” to their sin (as in Rom1:24,26,28). In contrast, throughout scripture clean or white garments represent a life devoted to the Lord. This is evident from Zechariah 3:3,5; Revelation 3:4,18, 19:14.
All this means that Isaiah 64:6 should never be used as an excuse not to give our best to the Lord. Faith is both completed and authenticated by works (James 2:14-26). So when we turn away from sin, relying on God's power to clean us, we are clean in his eyes (Isaiah 1:16). No amount of going through the motions makes up for a lack of loving obedience to the Lord (see Mal 1 and also Jer 13:1-11). There are many passages that demonstrate our spiritual poverty before God, such as Ephesians 2:8-9, but this is not one of them.