Luke's supposed profession would no doubt matter when interpreting his work as an author, if indeed he was the author. As the question says, tradition assigns Luke as author of the gospel that now bears his name and of Acts of the Apostles, but this is only tradition and these books were originally anonymous, remaining so until the second century. If there are good grounds for believing that Luke was not the author, or if there are good grounds for believing that Luke was not a physician, then our interpretation of this work should not be based on Luke's supposed profession.
What is the evidence that Luke the physician was the author of Luke-Acts?
Clearly, the author of Luke-Acts was an educated man, and the profession of physician would at least fit that criterion. It is only in the disputed Epistle to the Colossians that we learn that Luke was, supposedly, a physician:
Colossians 4:14: Luke, the beloved physician, and Demas, greet you.
However, Bart D. Ehrman believes that this was not the reason the Church Fathers chose Luke as the probable author of Luke-Acts. He says, in Forged, page 207, the idea that Luke was a Gentile companion of Paul comes from Colossians. He says there are three persons in Colossians who were Gentile companions of Paul: Epaphras, Demas, and Luke the physician (Col. 4:12-14). Of these, it seems unlikely that Demas could be the author, since we learn elsewhere that Demas "abandoned" Paul (2 Timothy 4:10). Epaphras appears to have been known as the founder of the church in Colossae (Colossians 1:5-7), a church that is never mentioned in Acts. That would be odd if its founder were the author. This leaves the Church Fathers with one candidate, Luke the physician.
However, a substantial majority of New Testament scholars believe that Colossians is pseudepigraphical. Scholarship was divided on the issue until the 1970s but has steadily moved towards rejecting Pauline authorship. Richard DeMaris (The Colossian Controversy, page 11) cites Raymond Brown, who estimated that by 1984, around 60 per cent of scholars thought Colossians inauthentic. John Barclay examines the evidence against Pauline authorship (Colossians and Philemon, pages 22ff) and says this is not decisive, but nevertheless Colossians is routinely bracketed out as deutero-Pauline, with the consensus accepting only seven letters as 'assuredly' Pauline.
If all this seems dry and insufficiently conclusive, it is interesting that:
- Colossians most closely resembles the style of Paul's Epistle to Philemon.
- Philemon is the only undisputed Pauline epistle to mention Luke
- Philemon and Colossians both contain salutations by Epaphras and Aristarchus, but Colossians strangely reverses their roles, possibly as a result of confusion by the author:
Philemon 1:23: There salute thee Epaphras, my fellowprisoner in Christ Jesus
Philemon 1:24: Marcus, Aristarchus, Demas, Lucas, my fellowlabourers.
Colossians 1:7: As ye also learned of Epaphras our dear fellowservant ...
Colossians 4:12: Epaphras, who is one of you, a servant of Christ, saluteth you
Colossians 4:10: Aristarchus my fellowprisoner saluteth you
What is the present consensus regarding authorship of Luke-Acts?
Uta Ranke-Heinemann says, in Putting Away Childish Things, pages219-220, that Protestant theologians in particular stress that Pauline theology is completely alien to Luke and especially to Acts. For this reason “Luke the beloved physician” and “co-worker” of Paul can not be the author of the Gospel according to Luke.
John Shelby Spong says, in Born of a Woman, page 109, the author of Acts would not have been Paul’s travelling companion because of the large number of discrepancies between Acts and Paul’s epistles.
The broad consensus of scholars is that Luke-Acts was written no earlier than the 90s of the first century, with a growing consensus that Acts belongs to the second century - much too late for Luke the physician.
In the light of the foregoing how should we interpret Luke-Acts?
First, even if Luke was the author of Luke-Acts, the profession of physician rests on the shaky ground of a disputed epistle. We therefore can not conscientiously use this information in reading and interpreting Luke-Acts.
Second, it is considered highly unlikely that Luke was the author of Luke-Acts. This means we should read these works independent of our understanding of Paul's theology, which in any case appears different from that found in Luke and Acts. Once we recognise that the author never met Paul, it becomes easier to understand the discrepancies between Paul's epistles and Acts. David Ravens (Luke and the Restoration of Israel, pages 174-5) discusses the views of some scholars that the author of Luke-Acts knew Paul's epistles but would have treated the letters no less creatively than he treated his other sources.