We usually think of Luke as being the least Jewish of the Gospels and geared toward the Gentiles. As I read over Luke, I am struck by the fact that in many ways, it is more Jewish than Matthew. For instance, Matthew's infancy stories include an account of the first act of worship to Jesus coming from gentile Magi. Luke mentions no Gentiles in his infancy account. Everyone is a Jew, and Luke is careful to show that they all fulfilled the law.
While Luke doesn't appear to quote as many Old Testament passages as Matthew in the infancy stories, he alludes to the Old Testament as much as if not more than Matthew.
Matthew and Mark both mention the feeding of 5,000 Jews in Jewish territory with 12 baskets left over as a sign, then 4,000 people in Gentile territory with 7 baskets left over as a sign. But Luke only mentions the feeding of 5,000 Jews. In fact, the whole context around the feeding of the 4,000 where Jesus ministers among gentiles is not mentioned in Luke.
One other subtle Jewish feature of Luke's gospel is how he models the infancy stories. It appears that Luke uses the stories of the birth of Samuel as a model to tell the stories of the births of Jesus and John the Baptist. The unusual births, the Songs, and the dedication at the temple all are reminiscent of the Samuel stories. Luke is masterful in the way he arranges the material by making subtle connections to his Jewish audience by arranging the material similar to an Old Testament narrative.
But there is yet another unique feature. Not only does Luke begin like an Old Testament narrative, it also reads like secular history. Luke used the conventions of history writing used by historians of the time. The introduction and dating are both typical of secular historical works. Luke mentions Roman officials more than other New Testament writers, which places the Gospel squarely in the context of the world around it. All of this would have given some credibility to the work for unbelieving Gentile readers and show the unmistakable universality of the Gospel, especially in volume two, the book of Acts.
So, is Luke a Jewish or Gentile Gospel? The answer is, "yes." Luke was masterful in arranging his material in a way that would reach both Jew and Gentile audiences. He was sensitive to the readers and how they would hear the story.
How sensitive are we to those who hear the story of the Gospel from us? How much do we take into account how people will see, hear, and understand us? How much time do we take to make points of contact with people, to relate the Gospel to them in a way that they would see its need, practicality, and relevance? How can we do this? One good place to start is by inviting your family and friends to small group home Bible studies. Unlike worship services, they will feel freer to ask questions and see us with our "hair down" so-to-speak, and experience Christianity in action in a way they would not in a worship service. I challenge you to consider ways to make the connection with family and friends with the Gospel.