"For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge?
God judges those outside. 'Purge the evil person from among you.'" - 1 Corinthians 5:12-13
Here is specific instruction from the Lord that the sins of this world (sexual immorality in this context) are not acceptable to be found among us. But on the other side of the coin, and perhaps more importantly, we are not to be judging or disassociating ourselves with such people who are not in Christ. If we do not associate with such non-believers, who will love them? Who will demonstrate the love of Christ to them?
Yet the seeming standard of operation for believers these days is to do exactly the opposite. In the news, and even from the pulpit you see Christians denouncing non-believers for the sins of the world. When we should be loving and not judging them. Likewise American churches, especially small ones, seldom practice church discipline. If we don't, even a little sin can destroy us from the inside (see verses 6 and 7). Our judgement is to be inward focused, not outward. Our love is supposed to be in both areas, but outward focused love should be void of judgement.
Love those outside the Church. Judge and deal appropriately with those inside the Church. For those who God already has their soul, he now wants their whole. For those who he does not yet have, He wants their soul, not their sin first. If we do not know the Lord, what motivation have we to care about truth? We care to live lives honoring to God because we've seen His glory. But non believers need to see His glory and His love before they will desire to honor Him in their own lives (and thus mortify sin).
The inward focus, which includes discipline, is to encourage the Holy Spirit to be at work in the lives of those in the church — thus improving our witness. The outward focus, which does not include discipline, is to love without condition, so others may know how Christ has loved us.