That shows how little you have read about Middle-Eastern history. Ishmael was the father of the peninsular Arab Bedouins -- from the Najaf or the interior part of the ARabian peninsular. Abraham's third "wife" -- Keturah, was the mother of the Midianites who lived in the Sinai (one of those was Moses' father-in-law, who's sub-tribe became part of the Israelites when the Israelites came out of Egypt.
What you call Arabs now are not of true, historical arab descent -- ARABS, that term truly means only those of Bedouin origin from the Najaf. Genetic studies have proven that the majority of people in Morocco, Tunisia, Libya, Algeria, even if they call themselves Arab are truly of Berber / Imazighen origin. Read that up. They underwent a period of Arabization due to Islam's teaching that essentially Arabs are the top caste and the Querishies, descendents of Mohammed are the top sub-caste of that caste.
People from Egypt are by and large from Coptic / Ancient Egyptian stock, people from Lebanon are Canaanites, from Syria are Arameans, from Turkey are Greek or Lydian or Galatian or Lycian or Armenian origin. People from Iraq are of Chaldean/Assyrian origin.
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Do Arab (Bedouins) Muslims have Jewish blood? Yes -- read about the early history of Islam. In Mecca and Medina you had large Jewish clans who controlled the business there. One of Mohammed's wife was a Jewess. You also had Ethiopian Christians (since Yemen was part of the Ethiopian Empire -- an Ethiopian General had attempted to conquer Mecca barely a decade before Mohammed), as well as Nestorian and Arian Christians, Zoroastrians and of course, the pre-Islamic Bedouin religion (worship centered around the Ka'aba which had statues of Allah/Ba'al Al'llah and his daughter Uzzat, Al'at and Amat).
Mohammed took elements from all these religions and created his mis-mash. He used this primarily to create a Bedouin Empire. The Bedouins then assimilated theJews -- many converted, many were forcibly converted. Hence the basic Muslim Arabs had Jewish blood