Well, the two trace back to a dispute over which of Abraham’s sons, Isaac or Ishmael, is the legitimate heir to God’s promise to him.
There was never a dispute between Abraham's sons, or their descendants, as to which of them was heir to any promises by God. Isaac's sons founded Judaism. Ishmaels went off and continued their pagan ways, for thousands of years. Then the tale was rewritten, that's all, like an alternative history that says that the South won the Civil War. Such a story does not create a dispute over who won, and someone who contends the south won is just a liar, or the follower of one. Same thing here.