Abraham is revered by the Jewish people, by Christians, by the Arab people, and by Muslims. God has made Abraham’s name great, and all the families of the Earth are blessed through his descendants.
Of whom is Abraham the father? He is the father of the Arabic people through his son, Ishmael, whose mother was Hagar, the Egyptian. Abraham is a descendant of Shem, a son of Noah. Hagar, as an Egyptian (Mizraim), is a descendant of Ham, a son of Noah.
Abraham is the father of the Israeli and Jewish people through his son, Isaac, and his grandson, Jacob. Isaac’s mother was Sarah; Jacob’s mother was Rebecca. These were all descendants of Shem. Jacob had a twin brother, Esau/Edom, who married two Canaanite women (descendants from Ham), and then married a daughter of Ishmael.
Abraham is called the father of many nations, and, indeed, there are many Arab nations, and one essentially Jewish nation. Even through his marriage to Keturah, after Sarah died, Abraham had sons through whom have come other ethnic groups, probably including the Bedouin.
What distinguishes the Jewish people’s relationship to Abraham over the others is that of YHVH God’s covenants to and through them, and not to or through the others.
Abraham is also the “spiritual” father of all who believe in Yeshua/Jesus as the Messiah/Christ and the Son of the Living God. That is, all who believe in God the Father and His only begotten Son, Jesus Christ/Yeshua the Messiah, are children of Abraham through faith in the God of Abraham, of Isaac, and of Jacob/Israel. Jesus, as a Man, was descended from Abraham, Isaac, and Jacob. Abraham believed that God Almighty, the Most High God, YEHOVAH, could raise the dead to life in order to fulfill His promises to and through him.
Not all who are called Christian are believers, just as not all Israel is Israel. Christian/Messianic believers can call Abraham their father, whether they are Jewish, Arab, or any other Gentile.
Muslims do not believe in YHVH, God of Abraham, of Isaac, and of Jacob. They do not believe that God is a Father, or that Jesus is His Son. If God is not a father, then He has no children. Jewish people believe that God is a Father, and that Israel is His first-born son (as a nation); but they do not believe that Yeshua/Jesus is the Messiah, whoever else they may think is. Christians believe that God is their Father, and that they are children of God through their faith in Him through Jesus, His Son, by the Holy Spirit who dwells within each born-again believer in Him.
The conclusion of this is that there are not three Abrahamic faiths — Judaism, Christianity, and Islam. Jewish people in the flesh (natural descendants) can call Abraham their father; natural Arab people through Ishmael and even Esau/Edom can consider Abraham their ancestral father in the flesh; but only those from whatever nation who believe in Yeshua/Jesus/Yasua as Lord and Christ/Messiah, the Son of God, have the same faith as Abraham. Yeshua said that Abraham saw His day, and was glad.
There is a wrongly placed sympathy towards Islam and Muslims by erroneously accepting Islam as an Abrahamic faith. Their God is not the God of Abraham. They need to repent and believe the gospel, and be set free by the truth, to worship the true living God in spirit and truth. Traditional Judaism does not accept that Jesus/Yeshua is the Messiah. They, too, need to repent and believe the gospel, and come back to the God of their fathers. Nominal Christians do not have living faith; also they need to repent and believe the gospel that their righteousness is from God and not from their religious culture or affiliation.