"For they being ignorant of God's righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God." (Romans 10:3)
The Bible clearly lays the case against trying to establish our own righteousness by our own works. Well meaning believers fall into the trap of trying to relate to God based on their own deeds. Unbelievers who acknowledge that they do believe in some sort of "god" fall prey to believing that God will accept them because they are a good person. The problem lies in the concept of righteousness. Romans 3:10 tells us that "There is none righteous, no, not one." Good deeds can't cover unrighteousness. If they could we wouldn't need a savior. 99 percent righteousness is still unrighteousness. The line is formed hard and fast.
Bur thanks be to God our Savior has made a way for us! Through Him we have the righteousness of God imparted to us by faith (Romans 3:22, Philippians 3:9). But what do we see in the human condition? We see such pride, arrogance and conceit formed in an unfounded and historically inaccurate view of the goodness of man. A view that manifests itself in people who believe that God must accept them because they are good. They refuse to submit to the righteousness of God. From the perspective of one who has been saved by the grace of God that is mind-boggling. Jesus has lovingly laid down His life and paid the price for us, but we refuse to accept the free gift He so willingly offers.
Christians who don't get this will live a Christian walk with a certain level of frustration, but thankfully it's not an eternal life and death decision for them. The grace of God is willingly extended to those who receive it by faith. We are saved by what we believe, and we're not disqualified by error in doctrine or belief in other matters. The grace of God is powerful. The true tragedy lies with those people who believe there is a God, but refuse to submit to what God has said. Those are the people who will try to pass muster by holding up their good works and will be tragically disappointed when told "I never knew you." In some ways those cases will be sadder than atheists who willfully argue against and reject God, but simply believing there is a God is just not enough. Even demons believe that.