While there's plenty of room for reasoned debate, an alternative view should consider a couple of facts in evidence, in my opinion. In Luke's writing of Acts Chapter 21, he relates that the Jews are extremely angry with Paul/Saul for bringing Gentiles into the Temple area. Except that the Gentile named as being brought to the Temple is Trophimus who is an Ephesian. And actually, Luke relates that Paul never really brought Trophemus to the Temple, but had been seen on the streets of Jerusalem with the man. If the Jews wanted to berate and possibly stone to death Paul for this behavior, they would have needed to look no further than Luke himself, since Luke clearly describes the interior of the Temple courtyards and indicates a great familiarity with the Temple mode of worship and conduct of the Chief Priest and others (Luke 1:8 to 20). It's apparent to some scholars that the reason for not attacking Paul on the basis of Luke's transgreesion into the Temple, is that Luke is a Jew, himself. Lastly, there's indepth consideration given to Luke's relationship with Mary, the mother of Yeshua. In order to gain the intimate knowledge of her (Luke 2: 19-51) and how she felt about her Son, Luke would most certainly have had to be a Jew. Again, I think there's ample room for discussion based on our knowledge of the "Good Doctor"...