Did God send the angel to save Ishmael so that Islam could exist since Moslems believe Ishmael is the father of the Arabs?
I would say this about the angel sparing Abraham's son, Ishmael. In his covenant with Abraham God promised that He would bless the seed of Abraham and those who blessed him (Genesis 12:1-3, etc.). I believe that God's blessing on Abraham was both general (all his physical descendants) and specific (through the designated "seed" of Abraham, starting with Isaac, then followed by Jacob, etc.).
Thus God spared Ishmael as a result of His general promise, but the blessings pronounced on Ishmael are certainly inferior to the covenant blessings pronounced on Isaac (compare Genesis 17:21; 21:12-13). We see that Ishmael was blessed, because he was the son of Abraham, but he was not the one through whom God's covenant blessings would be passed down. God kept His promise to make Ishmael a great nation of him (21:18), but that is the limit.
I am reminded of the fate of Jacob and Esau. By God's sovereign choice His covenant blessings passed through Jacob, not Esau (even though Esau was the first-born). Esau was given a blessing (Genesis 27:38-40), but it was decidedly inferior to the covenant blessing pronounced on Jacob (Genesis 27:26-29). In the blessing of Jacob he (Jacob) is told that his brothers would bow down to him (27:29).
In Romans 9:6-13 Paul shows how God sovereignly chose to bless Jacob over Esau, as He blessed Isaac over Ishmael. Thus, Islam is inconsistent with Scripture if it claims that the primary blessings of the Abrahamic Covenant were passed down through Ishmael. Was he born before Isaac? Yes. But so too Esau was born before Jacob. God had the right to choose the younger over the older (Genesis 25:23; 27:40; note Genesis 48:8-22).
Yes, God did preserve Ishmael's life, and He did bless him, but not as the son through whom the blessings of the Abrahamic Covenant would pass, not as the one through whom Messiah would come (Genesis 49:8-12).
Remember that God also used angels to rescue Lot, and through Lot's daughters two nations were begotten. But it was not through Lot that the blessings of the Abrahamic Covenant would pass (see Genesis 19).
Merely being a descendant of Abraham (as, indeed, Muhammad may have been) does not save anyone.
6 It is not as though the word of God had failed. For not all those who are descended from Israel are truly Israel (Romans 9:6).
It was not through Abraham's seed -- the nation Israel (as if "seed" were plural) -- but through Jesus (Abraham's "seed" is singular) that the blessings of God's covenant with Abraham come upon men (Jews and Gentiles and Arabs, who trust in Jesus):
15 Brothers and sisters, I offer an example from everyday life: When a covenant has been ratified, even though it is only a human contract, no one can set it aside or add anything to it. 16 Now the promises were spoken to Abraham and to his descendant. Scripture does not say, "and to the descendants," referring to many, but "and to your descendant," referring to one, who is Christ (Galatians 3:15-16).
Abraham's spiritual seed are all those, Jew or Gentile, who place their trust in Jesus as the promised Messiah, as God's only way of salvation:
13 For the promise to Abraham or to his descendants that he would inherit the world was not fulfilled through the law, but through the righteousness that comes by faith. 14 For if they become heirs by the law, faith is empty and the promise is nullified. 15 For the law brings wrath, because where there is no law there is no transgression either. 16 For this reason it is by faith so that it may be by grace, with the result that the promise may be certain to all the descendants-not only to those who are under the law, but also to those who have the faith of Abraham, who is the father of us all 17 (as it is written, "I have made you the father of many nations"). He is our father in the presence of God whom he believed-the God who makes the dead alive and summons the things that do not yet exist as though they already do (Romans 4:13-17).
26 For in Christ Jesus you are all sons of God through faith. 27 For all of you who were baptized into Christ have clothed yourselves with Christ. 28 There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female-for all of you are one in Christ Jesus. 29 And if you belong to Christ, then you are Abraham's descendants, heirs according to the promise (Galatians 3:26-29).
Now, did God intend for there to be Islam? God is sovereign as so Islam has come into existence because God chose to use it, just as He chose to use Pharaoh, who opposed His people:
17 For the scripture says to Pharaoh: "For this very purpose I have raised you up, that I may demonstrate my power in you, and that my name may be proclaimed in all the earth" (Romans 9:17).
False religions will be used of God to test the faith and fidelity of His own people:
4 Jesus answered them, "Watch out that no one misleads you. 5 For many will come in my name, saying, 'I am the Christ,' and they will mislead many" (Matthew 24:4-5).
10 Then many will be led into sin, and they will betray one another and hate one another. 11 And many false prophets will appear and deceive many, 12 and because lawlessness will increase so much, the love of many will grow cold.
13 But the person who endures to the end will be saved. 14 And this gospel of the kingdom will be preached throughout the whole inhabited earth as a testimony to all the nations, and then the end will come (Matthew 24:10-14).
Saying that God intended for Islam to exist is not saying that God meant for Islam to be a means by which men would find the forgiveness of sins and the gift of eternal life:
6 Jesus replied, "I am the way, and the truth, and the life. No one comes to the Father except through me" (John 14:6).
8 Then Peter, filled with the Holy Spirit, replied, "Rulers of the people and elders, 9 if we are being examined today for a good deed done to a sick man-by what means this man was healed- 10 let it be known to all of you and to all the people of Israel that by the name of Jesus Christ the Nazarene whom you crucified, whom God raised from the dead, this man stands before you healthy. 11 This Jesus is the stone that was rejected by you, the builders, that has become the cornerstone. 12 And there is salvation in no one else, for there is no other name under heaven given among people by which we must be saved" (Acts 4:8-12).
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