Frank Thielman suggests that there are three approaches that interpreters generally understand Luke’s view of the Law in Luke–Acts. He writes,
“Many interpreters claim that Luke's approach to the law is consistently conservative. Jewish Christians are required to keep it, and Gentile Christians, although not obligated to become Jewish proselytes, are brought under the Law's requirements by means of the Apostolic Decree in Acts 15. Some interpreters think that for Luke the law was the divinely sanctioned way of life for God's people until the introduction of a new era with the coming of Christ. Luke faithfully records in his two volumes that gradual acceptance among Jesus’ followers of the notion that a new age had dawned. One interpreter thinks Luke is anti-Semitic, and that his account of the abandonment of the Jewish law among the early Christians serves his attempt to show that the separation of Christianity from Judaism was the fault of the Jews.”
Frank Thielman, The Law and the New Testament: The Question of Continuity (New York: Crossroad, 1999), 136.