Jesus Christ became sin for us (2 Corinthians 5:21). The idea that God can't look upon sin is silly. Habakkuk 1:13, which seems to speak of this, refers to God not being able to look upon sin with approval. If God could not look upon sin then He would have never looked at the earth again after the fall. Jesus looked at sin over and over when He lived as a man on earth. To say God cannot look upon sin is like saying Jesus is not God.
Jesus is God. Is He less holy than the Father? Holy means pure and unmixed. People claim God is too holy to look upon sin. I say God is so holy that He can become sin and still stay pure and unmixed. That is a holiness beyond what we can imagine.
The good news is that because of Jesus, "God no longer charges people with sin" (2 Corinthians 5:19). God is not blind to help those in need out of sin or out of sinful ways yet He does not count people's sins against them.
God's View on Sin
Who's Counting? The Honest View of Christians & Sin in The New Testament