Q. Were all the twelve Apostles Jews?
A. We have no good reason from Scripture or Tradition to think otherwise. Some of the Apostles had Greek names, but this was not uncommon among Jewish people in the eastern Mediterranean region of that time, given that Hellenistic culture dominated that part of the world.
In addition, the Apostles all worshipped in the Jewish temple with Jesus (presumably in the inner courts where Gentiles weren’t allowed), and they celebrated the Passover meal and other Jewish feasts with Him. So we can confidently assume, I think, that all were Jewish.
It’s also important to note that the first Christians engaged in some internal debate over whether Gentiles (non-Jews) should be baptized and allowed to enter the Church (see Acts chapters 10 and 11). If one of the Twelve whom Jesus chose as Apostles had been a Gentile, it’s hard to see how this issue would have arisen as a controversy in the early Church.
Finally, keep in mind that even if, as it seems, none of the twelve Apostles was Jewish, Jesus seems to have had other followers (disciples) who were not Jewish — presumably, people such as the Canaanite woman (Matthew 15:21–28) and the Roman centurion (Matthew 8:5–13).