ESV, Colossians 4:
How likely is it that Luke was a gentile?
Highly likely. If Luke was a Jew, he would have likely been circumcised. But he was not circumcised.
With Paul at the time, Aristarchus, Mark, and Justus were the only circumcised men (Jews) among his co-workers.10 Aristarchus my fellow prisoner greets you, and Mark the cousin of Barnabas (concerning whom you have received instructions—if he comes to you, welcome him), 11 and Jesus who is called Justus. These are the only men of the circumcision among my fellow workers for the kingdom of God, and they have been a comfort to me.
Paul listed the Jews first, then Epaphras who was a gentile from Colossae.12 Epaphras, who is one of you and a servant of Christ Jesus, sends greetings.
Besides Epaphras the gentile, Luke and Demas were with Paul.He is always wrestling in prayer for you, that you may stand firm in all the will of God, mature and fully assured. 13 I vouch for him that he is working hard for you and for those at Laodicea and Hierapolis. 14 Our dear friend Luke, the doctor, and Demas send greetings.
How likely is it that Luke was a gentile?
Highly likely. If Luke was a Jew, he would have likely been circumcised. But he was not circumcised.