Hmmm...the Saviour I know promised to throw my sins into his sea of forgetfulness. The only good thing you can do to reach Heaven is accept Jesus as your saviour.
Could be a misinterpretation on your part, could be an oversimplified explanation of the non-judgment of a loving G-d. But they are great lyrics, aren’t they ;-)
It doesn’t mean that God is a non-judgemental God, - just that he doesn’t remember our sins if we accept the offering of his Son. Believers will be rewarded according to how they followed God’s Will.