There are times when the plain sense of one passage of Scripture contradicts the plain sense of another passage. An obvious example of this is Proverbs 26:4-5. When that happens, you can either decide that one passage is wrong, or, if you honor the authority of all of Scripture, try to look a little deeper to find out how the two passages are to be understood in a way that does justice to them both. For example, I conclude from the Proverbs 26 passage I just mentioned that there is no safe way to deal with a fool, for whether one answers him or not, you cannot avoid getting into trouble. The contradiction of the plain sense of the two verses is a way of highlighting the quandary we find ourselves in in this case.
One has to do the same thing with Jesus' warnings not to judge and the statements he and others make in Scripture urging us to judge. You can either assume that one of them is wrong (as you seem to assume Paul is) or you can try to honor both of them by looking a little deeper into them. If you assume Paul is wrong in 1 Cor 5, you also (it would seem), have to assume that a number of other "judgmental" passages in the NT are wrong as well, e.g. Gal 1:6-9, Romans 3:10-18, 2 Peter 2, 1 John 4:8. Since I'm unwilling to assume that any of the authors were in error in writing what they did, I assume that the judging Jesus forbids is not the judging that Paul, Peter or John are doing. In particular, I conclude that Jesus is talking to people with planks in their eyes who are making judgments against people who only have dust specks in their eyes. The planks may be spiritual pride, hypocrisy or any of a number of other very toxic sins, while the dust specks are probably things that may not be sins at all (e.g. styles of clothing or music). In any case, the person with the plank needs to realize that he will be examined by God as closely as he is examining his neighbor, and he may not like the results.
But when we have dealt with the planks in our own eyes (like Jesus says we should), we may be able to deal with the dust specks (or planks) in the eyes of others. This is what Paul is doing in 1 Cor 5, and what I'm claiming that we need to do more often than we are.
You have concluded that my primary target here is "the way the Church treats homosexual persons," and argued that the same approach that I use to justify judging can be used to justify homosexual behavior. You are welcome to try this, but I don't think it will work. For one thing, there are no passages in Scripture whose plain sense is "sex between two men or two women is ok." So you don't have anything that contradicts the passages in both the OT and NT whose plain sense is that such sexual behavior is wrong, and thus no justification for looking for a deeper meaning than the plain sense of these passages.
Absent any internal contraction of this sort in the plain sense of Scripture, you seem ready to resort to love or reason or to override the plain sense of Scripture. But it is neither loving nor rational to encourage people to do what Scripture forbids, regardless of how much they want to do it. If God says through Paul
Now the works of the flesh are evident: sexual immorality, impurity, sensuality, idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions, envy, drunkenness, orgies, and things like these. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God (Gal 5:19-21)then it is the height of irresponsibility to encourage people to go on with a little drunkenness, or bit of sorcery or some occasional sexual immorality on the assumption that their faith or other good works will override these sins and that God will forgive it all in the end. The truly loving and rational act is to warn people to stay away at all costs from these behaviors, because the pleasure that comes from them cannot possibly compensate for the loss of the kingdom of God. And if it takes ejecting some people from the church (and I do not restrict this group to the those who are sexually immoral) to make clear to them their peril (as Paul recommended in 1 Cor 5), then that is what love and reason should urge us to do. Though we can't say for sure, 2 Cor 2:5-8 appears to indicate that this strategy worked in Paul's case.