Y'shayahu / Isaiah 34:5-6 has the prophet foretelling that before the messianic age Jerusalem will rejoice over the downfall of Edom (Y'shayahu / Isaiah 34:5-6).
First a little background.
In the Torah Abraham's son Isaac had two sons: Esau and Jacob. Esau was the elder of twins, but he was said to be unworth: a womanizing idler with little interest in G-d or Torah, while Jacob was a kind, Torah observant man who loved G-d.
Esau was "in line" to inherit from Isaac, but in B'reshit / Genesis 25 he says: “I'm going to die anyway. What do I care about the birthright. Take it and give me the stew. And Jacob said, "Swear to me as of this day"; so he swore to him, and he sold his birthright to Jacob." (B'reshit / Genesis 25:31-34).
Esau was the ancestor of a nation called Edom, which tradition identifies with Rome. (Edom means red, like the color of blood or of Jacob's stew.)
Isaiah foretells the doom of Edom as does Bamidbar / Numbers 24:18-19. Y'shayahu / Isaiah 34:5-6 says: “Edom shall be possessed, and Seir shall become the possession of his enemies, and Israel shall triumph. A ruler shall come out of Jacob, and destroy the remnant of the city."
Edom (the nation from Esau, Jacob's brother) has long been an enemy to the Jewish nation. Our sages stated that Edom = Rome, and when the Roman Empire became the Christian empire it remained "Edom."
Why? Why do so many Jewish sages equate Edom with Christianity (Rome)?
Kimchi, Ibn-Ezra, the Rambam (with an "m"), the Ramban (with an "n") and Abarbanel to name but a few say that Edom = Christianity. The Ramban wrote in “Gate of Redemption” (written circa 1263 C.E.) "We...believe that we are presently in the exile of Edom (Rome) and that we shall have no respite from it until the coming of the Messiah. … The Edomites [the nation around Mount Seir, descended from Esau] were the first to mistakenly follow after the man who claimed that he was the Messiah.
"They also ascribed godliness to him. When they came to the land of Italy, their error spread to the nearby city of Rome. There in the days of Constantine who ruled over Rome …, the council under the authority of the bishop [of the city] of Rome determined their belief in (Jesus) and established it [as the religion of the empire].
"This, above all else, is the main cause and reason that Rome and Edom are considered as one kingdom although they are different nations. In spite of that [difference], they are related because of their uniformity of belief which makes them one people and one nation. … [The Sages of the Targum] thus explained that Rome is in Grecian Italy and that many of the Edomite people are contained therein. Hence, [Rome] is called “O daughter of Edom,” (Eicah / Lamentations 4:22)."
Interesting enough the Christian bible itself states that some of Jesus' followers came from Edom. Mark 3:8 states that Jesus' disciples came from the lands populated by the Edomites. "When they heard about all he was doing, many people came to him from Judea, Jerusalem, Idumea (Edom), and the regions across the Jordan and around Tyre and Sidon." Mark 3:8.
Does this mean that Ishmael and Esau are somehow doomed?
Of course not. Everyone alive can turn to G-d at any time. We can choose to sin or do good. . . So while the prophet Malachai in 1:3 says "And I hated Esau, and I made his mountains desolate and his heritage into [a habitat for] the jackals of the desert" this does not mean that G-d hates all of Esau's descendants. R' Kook (1865 - 1935) wrote "Noteworthy in this respect is the statement of Rabbi Elijah Gaon on the verse, “But Esau I hated” – “this refers to the peripheral part of Esau, but the essential part of him, his head, was interred with the patriarchs.” It is for this reason that the man of truth and integrity, Jacob, said [on his reunion with Esau], “I have seen you, and it is like seeing the face of G-d” (Gen. 33: 10). His word shall not go down as a vain utterance. The brotherly love of Esau and Jacob, Isaac and Ishmael, will assert itself above all the confusion that the evil brought on by our bodily nature has engendered. It will overcome them and transform them into eternal light and compassion." (Letters, 1, 112).
The Torah tells us that Jacob and Esau as well as Isaac and Ishmael, were eventually reconciled, In the messianic age former Christians and Muslims will all be united, along with Jews, in their love for G-d and their fellow man.
Remember that Esau was Jacob's brother -- just as Ishmael (Islam) was Isaac's brother. We are all related at a very important level and the destruction of Edom does not mean the deaths of Christians, but rather the realization will come to them (as we are told in the T'nach) that there is only one G-d and they will reject the false quasi-paganism that put a veneer on the T'nach to discover the one true G-d.
Zechariah 8 "So said the L-rd: I will return to Zion, and I will dwell in the midst of Jerusalem; and Jerusalem shall be called the city of truth, and the mount of the L-rd of Hosts [shall be called] the holy mountain. . .
"So said the L-rd of Hosts: As it will be wonderful in the eyes of the remnant of this people in those days, it will also be wonderful in My eyes, says the L-rd of Hosts. . .
"So said the L-rd of Hosts: Behold I will save My people from the land of the east and from the land of the west (Christianity and Islam). . .
"And I will bring them, and they shall dwell in the midst of Jerusalem; and they shall be My people, and I shall be their G-d, in truth and in righteousness. . .
"And many peoples and powerful nations shall come to entreat the L-rd of Hosts in Jerusalem, and to pray before the Lord. . .
"So said the L-rd of Hosts: In those days, when ten men of all the languages of the nations shall take hold of the skirt of a Jewish man, saying, "Let us go with you, for we have heard that G-d is with you."