I equate islam to Orwell's "1984" where they (muhammad) took the Torah and the Bible and crossed out what they didn't like and added what they did.
I don't care their belief of descending from Ishmael.
But that's besides the point.
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I referenced Esau [Edom] not Ishmael. Jacob and Esau's father was Isaac; Ishmael would've been their uncle. Your argument relies on the muslims' belief Ishmael was offered up and not Isaac. My argument is Isaac was offered to God by Abraham, as it is written in the Bible, and that Jacob and Esau were Isaac's son. Further my argument is the Jews descended from Jacob (loved by God) and the Arabs descended from Esau (hated by God).
Insomuch as belief goes, I don't care the muslims believe the descended from Ishmael as their patriarch or that he was offered to God as a sacrifice; their book is one of lies.
Esau's participation in the destruction of the Temple Which, the muslims of today believe they have claim to that ground as their birthright.
Wiki for a map of Edom's location
"Jacob I have loved, but Esau I have hated" Malachi 1:2-3 and Romans 9:13
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"The sons of Eliphaz, the firstborn son of Esau, were Chief Teman, Chief Omar, Chief Zepho, Chief Kenaz, Chief Korah, Chief Gatam, and Chief Amalek
"But as for Ishmael, I have heard thee: behold I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation." Genesis 17:20
It makes no sense for Ishmael to have God's blessing and for Ishmael to be at war with Israel. It does however make sense that an outcast nation at war since the womb would descend into people that pervert God's Word and continue a millennium jihad that they were cheated from their birthright.
I believe there is pretty strong evidence that arabs/muslims descended from Esau and Biblical reason for their war.