Habakkuk 1:13a says, “You are of purer eyes than to behold evil, And cannot look on wickedness…” That certainly implies that God cannot look at sin. However, that is not what the verse means.
The next sentence reveals that God does look upon sin: “Why do You look on those who deal treacherously…” (Hab 1:13b). “Those who deal treacherously” would be sinning, so it would be a contradiction if it were true God that can’t look on sin.
The proper understanding comes in reading what comes next. After asking, “Why do You look on those who deal treacherously…” Habakkuk added, “And hold Your tongue when the wicked devours a person more righteous than he?”
Habakkuk 1:13 is really saying that God’s eyes are too pure to look upon sin and tolerate what He sees. God will judge all sins. But He will do so in His time and in His ways.
This explains how the Holy Spirit can dwell inside Christians who continue to sin. Their sins have already been judged by God, paid for by Jesus, and fully forgiven. In God’s eyes, a forgiven sinner is positionally righteous and secure. However, in continuing to sin, a Christian still needs to confess sins to be cleansed and restored to closer communion with God. The sins Christians commit cannot break their union with God, but will harm their communion with Him. Confess and be cleansed:
1 John 1:9 What is the Christian “Bar of Soap?”
What you need to know about Sanctification & Glorification