The scriptural basis for this belief comes primarily from Isaiah 64:6,7 which reads, "But we are all as unclean things, and all of our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities like the wind have taken us away. And there is none that calleth upon thy name that stirreth up himself to take hold of thee, for thou hast hid thy face from us, and hast consumed us because of our iniquities."
The understanding of this verse is that even our most righteous efforts are viewed by God as being filthy. More than that, they believe this verse says there is no one who truly calls upon the Lord or seeks after Him because we are all sinners, filled with iniquity, whose natural tendency is to rebel against God. Since God cannot abide in sin, He has hid His face and turned His back on us and we will be consumed (burn in hell) because of our wickedness. Then, based on this interpretation, they further conclude that man is incapable of doing anything truly righteous on his own and that righteous behavior can only occur when God is allowed to do His own righteousness through man.
This interpretation seems to fit what these verses are telling us, but as nearly all students of the Bible agree, to properly understand the meaning of any verse of scripture we need to put it in its proper context. To do otherwise would be to make it say something other than what the author intended for it to say. To see if this interpretation is consistent with what Isaiah is trying to tell us, we need to look at these two verses in context. And to do that we need to start back in chapter 63.
Isaiah begins by recounting the loving kindness that God has shown His people, the House of Israel (v7). He refers to Israel as God's sons, and says that God is their redeemer (v8). He says that when they were afflicted, God was afflicted along with them and that He sent His angel to save them. In His love and pity for them He redeemed them (v9). But instead of being grateful, Israel rebelled against their God and vexed, or grieved His Holy Spirit. Because of this, God turned His wrath on them and became their enemy and fought against them (v 10). Isaiah pleads with the Lord to remember His former zeal for Israel and asks why He has restrained His mercy and compassion toward them (15). He reminds the Lord that He is their Father and their redeemer (v16), but laments that even though they once possessed His Holy sanctuary (the temple) (v18), now God treats them no better than those who never knew Him, whom God had never ruled over, and who were never called by His name (v19).
Then in chapter 64 Isaiah continues speaking to God, almost in prayer fashion, pleading before the Lord in behalf of his people. He acknowledges how God comes forth to meet those who take pleasure in doing works of righteousness and who remember His ways. He further acknowledges that those who continue in keeping His commandments shall be saved. But then he laments that the House of Israel has not done this. Instead, they have sinned (v 5). He says that the entire nation of Israel has become sinful and unclean. Although they go through the motions of burning incense, offering sacrifices, praying to God, and keeping the various holy days mentioned in the Law of Moses, God has come to look upon these outward religious observances as being filthy before Him (see Isaiah 1:11-31). Isaiah admits that for all of their outward religious expressions, there isn't one of God's chosen people who truly seeks after Him. They have all turned their back on Him and every man does what he thinks is right. Therefore, God has turned His back on them (has hid His face from them) because of their iniquitous behavior. (v 7).
This has been the constant theme of Isaiah throughout his book. Beginning in the very first chapter he says that the ox knows his owner and the ass knows his master's crib, but Israel does not know their God (v. 3). He says that Israel is a sinful nation, a people who are laden with iniquity whose children have corrupted the ways of God and have forsaken the Lord. They have provoked Him and gone away from Him (v 4). The nation of Israel is described as their whole head being sick and their whole heart is faint (v5). From the sole of its foot to the top of its head the nation of Israel has no soundness to it (v6). What was once a holy city has now become a place of harlots. The Lord Himself says that it once used to be a place full of righteousness and justice but now it has become full of murderers (v 21). Their princes are rebellious and have become the companion of thieves (v 23).
Yet, despite all of this, continuing in chapter 64 Isaiah reminds God that He is their Father (v 8) and pleads with Him not to be angry with His people and to remember their iniquity no more. He again reminds God that they are His children. (v 9). He asks the Lord to return the land of their inheritance that has been taken from them (v 9. He talks about how the holy city of Jerusalem has been destroyed (v 10), and how the temple where their fathers once praised God has been burned to the ground (v 11). Then Isaiah begs mercy from the Lord, asking Him to refrain from afflicting His people so sorely (v 12).
In chapter 65 God answers Isaiah's prayer. He says that He had continually stretched forth His hand to His people, but they continually rebelled against Him, doing that which was not good rather than keeping His commandments. (v 2). He said that because of such behavior, they had provoked Him to anger. And what was it they had done to provoke Him? They "sacrificeth in gardens, and burneth incense upon altars of brick which remain among the graves, and lodge in the monuments, which eat swine's flesh, and broth of abominable things is in their vessels" (v 3,4). This has reference to religious rituals associated with false gods (idol worship). The Law of Moses commanded that they should not worship any other God and they had violated that command. Moses also said they should not eat swine or other unclean animals but Israel at the time of Isaiah had violated that commandment as well.
God then reminded Isaiah that their fathers had done the same thing when they "have burned incense upon the mountains, and blashemed me upon the hills." (v 7). Because of this blasphemous behavior, God had brought other nations to slaughter the Israelites in great numbers by the sword. He reminded Isaiah that when He called out to them, they (the Israelites) didn't hear Him. When He spoke to them, they didn't listen. Instead, they delighted in doing that which was evil rather than choosing to do that which God delighted in. (v 12)
God then said that His servants - those who obey Him - would not go hungry or thirsty and would rejoice, while the other people of Israel (God's chosen people who were disobedient) would be put to shame (v 13). God's servants will sing for joy, but the others will cry out and howl from the anguish of their heart because of their afflictions (v14). God says that His people will become cursed and He will slay them (v 15).
This is the context in which Isaiah said that all of our righteousnesses are as filthy rags.
Clearly, contrary to the common Protestant belief, this verse is not referring to mankind in general. Rather, it is talking about God's chosen people! When Isaiah talks about our righteousness being as filthy rags, he is directing his remarks at the believer in God, not the unbeliever! He is talking about people who claim to believe that God is their Father, Savior and Redeemer and who consider themselves to be His children but who don't follow His commandments. That means Isaiah 64:6 also applies to saved Christians as well! It is their righteousness that God considers to be as filthy rags. And why? Because they go about pretending they are holy and righteous but, rather than keeping God's commandments, they worship God in vain, teaching for doctrine the commandments of men (Matt. 15:9).
If we look at the New Testament we see the same thing happening during the days of Jesus. The Pharisees considered themselves as behaving righteously and scrupulously keeping God's commandments. However, Jesus said they were like whited sepulchres, outwardly acting holy but inside they were full of all manner of uncleanness (Matt. 23:27). Jesus taught that unless our righteousness exceeds that of the Pharisees we will not enter into the kingdom of heaven (Matt. 5:20). This is the kind of unrighteous behavior Isaiah means when he talks about filthy rags.
We have to remember that the Pharisees were the religious leaders of their day. They were the ones who claimed to believe in and worship the one true living God, yet for all of their pious talk and behavior, there was not one of them who truly sought God. This is evidenced by the fact that when the God they claimed to worship actually came among them, they rejected Him and put Him to death.
The filthy rags of unrighteousness which Isaiah talks about refers to the behavior of those believers in Christ who have an outward form of godliness, but who deny the power of God. And it is from these kinds of people that God turns away from (2 Tim. 3:5). As with Israel, it is upon His own chosen people who don't obey Him that God sends down His wrath (1 Pet. 4:17). And, as with Israel, those believers who fail to hear God when He speaks and who refuse to answer when He calls, He will cast them aside and call others who know Him not and invite them to the marriage feast (Matt. 22:2-14; see also Matt. 8:12).
When read in context this is what Isaiah means when he says that all of our rightesounesses are as filthy rags.