HURCH members should handle the conflicts which arise (in our interpersonal relationships with other believers) in house (vs. 1-8). Paul condemns Christians who sue one another under the eyes of secular judges. A foolish Christian should be better equipped to settle disputes among believers than an unregenerate judge. Believers can even forget justice for themselves altogether (no vengeance or self-justification). We should be willing to suffer mistreatment from our fellow believers (vs. 7). Jesus set the example for us. But if we are too weak spiritually to forgive our friends outright (and if we can't persuade them to make things right with us), then in a worst-case scenario, we should get help from within the congregation. It certainly makes no sense to for God's children to fuss and fight in front of the world.
Also, there is a clear list of vices that should be carefully avoided by church members. Having reminded the Corinthians that the heathen are not well equipped to judge believers, Paul reminds them of the kinds of things that are common in the world, things which should be absent in the church: heterosexual looseness, worship of anything or anybody other than God, infidelity, effeminacy among men, homosexuality, thievery, covetousness, drunkenness, insulting speech, and unfair business practices. Just because I am safe from hell doesn't mean I can use my safety selfishly. The God-shaped hole in my heart can only be filled properly, completely, and satisfactorily with God's dominating presence (vs. 13, 17 & 19-20); sin will never suffice.