I'm don't think Titus was a Jew he was a Gentile convert.Jesus was a Jew. The early followers of Christ were ALL Jews. EVERY individual who wrote ANY part of the Christian New Testament was a Jew. EVERY follower of Christ, for the first 10 years of the Christian church, was a Jew.
1st Corinthians 5: 11-13 is an interesting read on judging. My take is if they are not a Christian, then they are on the outside so God will judge them. If they are Christian and part of your group you may have to judge them in order to "put away from yourselves the evil person.