Does I Corinthians 6 teach that we are to judge each other? If we are to judge the angels, then should we judge others?

I Corinthians 6 (NIV) begins:  “If any of you has a dispute with another, dare he take it before the ungodly for judgment instead of before the saints…. If you are to judge the world, are you not competent to judge trivial cases?” (verses 2, 3)  The Apostle Paul is here referring to disputes within the church, where some believers had actually gone to court against their brethren in Christ.  Paul continues, “The very fact that you have lawsuits among you means you have been completely defeated already.  Why not rather be wronged?….” (verse 7)  In other words, turn the other cheek.  

In Matthew 18:15-17, Jesus instructed the injured person to humbly try to settle things with the alleged guilty person.  If the guilty person will not listen, even in the company of one or two witnesses, the matter should come before the whole church, but not be brought to public trial. Paul reminds believers that if they will judge men and angels in the next age, they should learn to use scriptures now to judge what is right or wrong in day-to-day matters within the church. However in this present life, we are not judge the world: “God will judge those outside.” (I Corinthians 5:13, NIV)

Our Lord Jesus also said, “Do not judge so that you will not be judged” (Matthew 7:1 NIV).  So how do we harmonize Matthew 18 with Matthew 7? In Matthew 7, Jesus was primarily speaking to those who abused the principle of “judgment” to make themselves look more righteous. Jesus continues, “You hypocrite, first take the plank out of your own eye,” in order to see how to help your brother (verse 5). Paul agrees with Jesus's words in Romans 14:1-12 (NIV), reminding us not to look down on our fellow Christians. We cannot see into our brother's heart, and if we are aware that a brother is struggling against a particular sin, we should show mercy.

But there is a legitimate use of judgment when sin threatens to disrupt the church or cause harm to a member.  “All scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness…” (2 Timothy 3:16,17 NIV)  In the same chapter that Jesus tells us "Do not judge," he warns us to beware of insincere Christians, saying, “By their fruit you will recognize them” (Matthew 7:16, 20 NIV).

Paul knew that it would be harmful for a congregation to tolerate obvious, deliberate sin.  He says, “Don't you know that a little yeast