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This is a controversial passage with the controversy revolving around what Paul meant by “inherit the kingdom.” Is this equivalent to “entering the kingdom,” or “to reigning in the kingdom” in the sense of inheriting one’s privileges as rewards for faithfulness?” At any rate, read the verses that follow, “Some of you once lived this way. But you were washed, you were sanctified, you were justified in the name of our Lord Jesus Christ and by the Spirit of our God” (6:11). Paul is not saying that such past behavior disqualified them from present service. The fact was, many of the Corinthian believers were living like unbelievers (see 3:6) and he was simply showing them just how contradictory the way they were living was because of who they were in Christ. It illustrated the gap and contradictory nature that existed between the Corinthians’ future position as those who could have the privilege of reigning with Christ and sharing in the kingdom and their present practice. The wicked (those acting unrighteously) would be in the kingdom (if truly believers), but they would have no share in the rewards of the kingdom because they were living unfaithfully (cf. 1 Cor. 3:12-15). Even if Paul were talking about entering into the kingdom, he was simply showing the contradictory nature of the lives of many if not most of the Corinthian believers as a strong motivation for change. He was not questioning their salvation or saying they could lose their salvation. He was saying that to live like an unbeliever is totally inconsistent with who you are in Christ.
So, in no way was he talking about qualifications for leadership. Certainly anyone living like this is not qualified to lead while in such a carnal state.