It affects who gets to migrate to Israel.
The 20% of Israelis who are Christian, Muslim and Druze Palestinians/Israeli Arabs (as oppose to Palestinians who live in the occupied West Bank andGaza) have the same civil rights as Jewish Israelis. However, a lot of jobs are reserved for military veterans Jews and Druze have to do national service other Arabs don't. This is further complicated by the fact that some Bedouin join the army and many Ultra Orthodox Jews refuse to.
Palestinians living in East Jerusalem which was occupied and annexed by Israel after the Six Day War and Syrian Druze living in the annexed Golan Heights were granted permanent residency which includes and the right to apply for full Israeli citizenship.