Paul was through and through a Hellenistic Jew---never was not a Hellenistic Jew. Died a Hellenistic Jew who was a follower of Jesus. As were the writers who wrote in his name. Plagiarism wasn't then what it is today. In any of the non-Pauline epistles, it's difficult to know who exactly wrote them. When Paul writes of certain people, quite often it's written, "born a Jew like me." Whoever wrote some of the non-Pauline epistles wrote, though, as if they were Paul (the Hellenistic Jew who followed Jesus, who was born a Jew and died a Jew.) Did Paul think followers of Jesus could be Gentiles? Obviously.
Did Jesus think that? Um...he came for the lost sheep of Israel, the writer writes in one part. Then there is that strange story about the Syro-Phoenician woman. (In same piece as "I came for the lost sheep of Israel)---and she talks about taking the crumbs. Please help my child. She pesters Jesus, basically and he seemed to be teachable
Still was pretty dismissive and nasty to her initially.