"Jacob I loved, Esau I hated."
The Edomites are a subsumed culture. They either were converted to Judaism or they became Muslim through the Islamic conquest.
http://www.jewishencyclopedia.com/articles/7972-hyrcanus-john-johanan-iHyrcanus, who had been confirmed by the Romans in the possession of the important seaport of Joppa, subjugated other Syrian towns, such as Berœa (Aleppo). He marched against the fort of Madaba, on the banks of the Jordan, which had always been hostile to the Hasmoneans, and conquered it after a six months' siege; he also conquered the town of Samaya (Samega), on the Sea of Galilee, of special importance on account of its geographical position. He then proceeded against the Samaritans, who had always sided with the enemies of the Jews. He conquered Shechem, one of the most important towns of Samaria, and destroyed the temple on Mount Gerizim (21st Kislew = December, about 120).
After victoriously ending the war in Samaria, he proceeded to subdue the Edomites, always a menace to the southern parts of his domains. With funds which he is said to have obtained from David's sepulcher he hired foreign troops, dismantled Adora and Marissa, the strong places of Edom, and forced the Edomites to accept the Jewish religion and submit to circumcision. This is the first instance of forcible conversion in Jewish history. In this Hyrcanus allowed his zeal for the Jewish cause to lead him to take a step which later wrought harm; for to the Edomites belonged the family of the Herodians, who were to bring about the ruin of the Hasmoneans. The Samaritans, who still held their strongly fortified metropolis of Samaria, with a part of Jezreel, remained hostile toward the Jews. For this reason Hyrcanus renewed his attacks upon them. He marched against Samaria at the head of a great army, but as his presence in Jerusalem was necessary, he left the siege of the former city to his two sons, Aristobulus and Antigonus.
In Malachi, the future fate of the Edomites is made clear:
Malachi 1:3-5
...but Esau I have hated. I have laid waste his hill country and left his heritage to jackals of the desert.” 4If Edom says, “We are shattered but we will rebuild the ruins,” the LORD of hosts says, “They may build, but I will tear down, and they will be called ‘the wicked country,’ and ‘the people with whom the LORD is angry forever.’” 5Your own eyes shall see this, and you shall say, “Great is the LORD beyond the border of Israel!”
It is actually a false teaching among some Christian circles that teach that in the latter days, the Edomites are supposed to dominate the Jews. They hearken to the teaching that the Edomites are supposed to throw of the harness of Jacob in Isaac's blessing to Esau:
Genesis 27:40
You will live by your sword;
you will serve your brother.
But when you grow restless,
you will tear away his harness
from your neck.”
I believe this was basically fulfilled when Judah fell to the Babylonians and the Edomites did nothing to assist the Jews. But Malachi was fulfilled when Hyrancus forced the Edomites to convert to Judaism.
Finally, Edomites may be Muslims, but not all Muslims are Edomites. We are meant to make peace with Islam and to try to eventually convert those that will to be Christians. The Imams (man) twists the Quran into violence. The Quran actually teaches that Muslims should be at peace with "People of the Book". "People of the Book" are people of the Bible, Jews and Christians. Muslims were to be violent in the Islamic conquest against the pagan Arabic polytheistic tribes, not against People of the Book. Nevertheless, the Bible does foretell the behaviour of the Muslims (descendants of Ishmaelites) in Genesis 16:12:
He shall be a wild donkey of a man,
his hand against everyone
and everyone’s hand against him,
and he shall dwell over against all his kinsmen.”
The Palestians must learn to accept that the West Bank belongs to the Jews and that Jerusalem belongs to the Jews, with Muslims being allowed in Jerusalem, peacefully. In return, the Jews should consider letting the Palestinians govern the Gaza strip. The Gaza strip has long been a thorn in Israel's side from the days of Judges when the Philistines occupied the region. Allowing Palestinian governance of Gaza should allow Jews and Palestinians to peacefully coexist. If the Palestinians do not accept this olive branch of peace, then the Jews should forcefully take back the Gaza strip.
The Bible tells that the Jews and Muslims are meant to coexist peacefully: In Isaiah 60, far, far after the time of Ismael's sons Nebaioth and Kedar, Isaiah prophecies:
All Kedar’s flocks will be gathered to you,
the rams of Nebaioth will serve you;
they will be accepted as offerings on my altar,
and I will adorn my glorious temple.
That basically is saying that Muslim (the sons of Ishmael, Kedar's and Nebaioth's) flocks will be accepted as offerings on the altar of the Holy Temple of Zion. That is a hallmark of peace, not enmity.
Trust me, no man taught me these things.
As far as Esau's relationship to Ishmael, Esau took wives from the Ishmaelites because he saw that Isaac and Rebekah disapproved of the Caananite women. To his credit he took wives from the Ishmaelite women who were under the covenant of circumcision instead of the pagan Caananites. If God did not want Islam and Judaism to coexist, he would have wiped out Hagar and Ishmael and the entire middle east would be Jewish instead of mostly Muslim. They would have died in the desert, but that didn't happen. If He didn't want us to try and convert Muslims to Christians, the Muslims would not accept Jesus as a prophet, and Lot's wife would have been turned to dust, not salt. Salt signifies a covenant of friendship in the Middle East.