Bible scholars commonly identify Luke as a Gentile. The proof that is given is the passage in Colossians 4:10-14. Verse 11 states in part: "And Jesus, which is called Justus, who are of the circumcision." The fact that Paul identifies those in verses 10-11 as being "of the circumcision" is used as proof that everyone listed after that statement is a Gentile. However, no direct statement of that kind is made in the text and Luke is mentioned three verses later after the general phrases including "them that are in Laodicea, and them in Hierapolis" (v.13). This would mean that all those in Laodicea and in Hierapolis were Gentiles (or that Paul
only greeted the Gentiles in these two cities). In other words, the proof is very weak.
I cannot prove conclusively that Luke was not a Gentile, but I believe that the teaching that he has to be one is built in a cloud of smoke. Another form of Luke is Lucius. In Romans 16:21, we find a Lucius who was one of Paul's kinsmen. Though this is probably not the same Luke, it is a [Luke] who was definitely a Jew--being related to the Jewish Paul. Luke, therefore, is not an exclusively Gentile name.
A couple of other lines of reasoning support the idea that Luke was a Jew. In the introduction to the book of Luke, Luke introduces the information he is giving with this statement: "Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word." Here, Luke includes himself as one of the eyewitnesses which were from the beginning. Perhaps the beginning here refers to the early work of the apostles, but this still tends to identify Luke as a Jew. The earlier the time, the greater chance that the person was a Jew. The door to the Gentiles was not fully opened until Acts 10. No matter what, Luke was an eyewitness that could trace his understanding of the gospel of Christ back to the beginning. He must have been a Jew.
A second line of reasoning develops from the authors of scripture. Romans 3:2 mentions the chief advantage of the Jews as the fact "that unto them were committed the oracles of God." That is, scripture came into the world by way of Jewish authors. This is true of the Old Testament, and as a rule, it seems to apply to the New Testament. God used the Jews to deliver His words to this world. That is, unless Luke was a Gentile. This would not be a small exception. Rather, this would be a major departure from God's pattern. Luke was the human author of Luke (24 chapters) and of Acts (28 chapters). If Luke is a Gentile, then one/fifth to one/fourth (his chapters are long) of the New Testament was written by a Gentile. Yet God states that the oracles of God were committed to the Jews.
In conclusion, do not be hard on those who still teach that Luke is a Gentile. They are only teaching what they have heard. Perhaps they are even convinced by the flimsy proof of Colossians 4:10-14. (Though most are only repeating what they have heard.) However, rest assured that the Gentile identity of Luke is not the settled "fact" that it is assumed to be. Actually, there is much cause to believe that he was indeed a Jew.