Jews believe that the lives of the Prophets are a foreshadowing of our own (ma'aseh avot siman l'vanim, as discussed by Ramban and others). What do the lives of the patriarchs tell us about the birth of Islam? In fact they tell us a great deal; and we can learn from them that we, as Jews, should not shun or fear the growth of Islam, but should welcome and embrace it as the natural extension of history.
First, what was the story of the Patriarchs? (Please note that I will be citing exclusively Jewish sources, to appeal to a Jewish audience). Abraham took two wives, as we know: Hagar (later called Qetura: Bereshit Rabbah 61:4, Rashi, etc) and Sarah. As we know, both women were princesses. We know that Abraham sent Hagar away at the demand of Sarah, but continued to visit her in the desert. A midrash (Arabic equivalent: hadith) about these visits is as follows:
Ishmael married and had four children and he prospered and had flocks and herds and tents according to the merits of Abraham his father. Some time after his father sent him away - perhaps three years – Abraham said to Sarah, “I will go and see my son Ishmael; I yearn to see him, for I have not seen him in a long time.” Sarah agreed, on one condition: that Abraham not dismount from his camel [so that he would not resume relations with Hagar, to whom he was still married]. Abraham went and he reached the place where Ishmael lived. There, he met Ishmael's wife. He greeted her and asked her, “Where is Ishmael?”
She answered, “Off, hunting game.”Still mounted on the camel Abraham said, “My daughter, give me a little water, that I may drink, for I am weary from the journey; and a little bread.” Ishmael’s wife answered, “No water, no bread.” The Midrash says that all this time while she was talking with Abraham, she also was beating her children in the tent, cursing them and cursing Ishmael. So Abraham said, “When your husband returns tell him, ‘A very old man from the land of Canaan came here to seek you. I did not ask him who he was, and seeing you were not here he spoke to me and said, ‘When Ishmael your husband returns tell him, Put away this tent pin, which you have placed here, and put another tent pin in its place.’" And thereupon Abraham returned home. Ishmael finally returned to his tent. Hearing this message from his wife, he knew the visitor was his father and that the "tent pin" referred to his wife. He immediately divorced her and married another.Another three years passed and Abraham said, “I will go see Ishmael, my son, because I have not seen him for a long time.” He made the same agreement with Sarah and he went off on his camel again. He met the new wife; and some say her name was Fatima. This one invited him in and offered him food and drink. He could not dismount, because of his promise to Sarah; so the woman brought him water and bread. Abraham told her, “Tell your husband, ‘A very old man from the land of Canaan came here and asked for you and I brought him food and water, and he ate and drank and his heart was glad.’ And tell him, ‘Your tent-pin is very good. Do not put it away from the tent.’” And Abraham went on his way and returned to Sarah.Ishmael returned again and Fatima repeats all this to him. And here the Midrash says, “Ishmael realized that his father still loved him.” Even though Ishmael had not seen Abraham, he knew his father was periodically checking in on him; that he was concerned with his welfare; that he had not forsaken him.
The immense love of Abraham for Ishmael is evident in this narative; as is Ishmael's obedience to Abraham, even while they were separated. But during this time, the Rabbis tell us that Hagar's heart was not faithful to God while in the desert, and that she complained against Him: "Yesterday thou saidest: 'I will multiply thy seed exceedingly' [Gen. xvi. 10]; and now my son is dying of thirst" (although it is well worth noting that Hagar remained faithful throughout this period to Abraham). This time of Ishmael in the desert is the time of b'nei Yishma'el before Mohammad. Most had relapsed back into idolatry; idols filled the Kabah and Mecca.
Returning to the narative of Abraham, when did the restoration of Ishmael and Qetura occur? In Parshat Chayei Sarah, we read וַיֹּסֶף אַבְרָהָם וַיִּקַּח אִשָּׁה, וּשְׁמָהּ קְטוּרָה. And Abraham took another wife, and her name was Qetura, because her deeds had become like Qeturot, incense (Midrash Rabbah). Ishmael and Qetura then lived with Abraham until his death (as per Bereshit 25:9). And when was the death of Sarah, but after the akidah? Now, therefore, the akidah was the destruction of the Temple, for there has been no greater loss to our people; and the death of Sarah was the loss of the semchiha in the fourth or fifth centuries C.E. And it was only after this that Mohammad, peace and blessings be upon him, was sent to the world. The proper response of b'nei Israel is to accept the return of their brother and to receive him again into the family, as it was in the beginning: וַיִּקְבְּרוּ אֹתוֹ יִצְחָק וְיִשְׁמָעֵאל, בָּנָיו, אֶל-מְעָרַת, הַמַּכְפֵּלָה And when these two live in peace, a new era will dawn.
וְהָיָה יְהוָה לְמֶלֶךְ, עַל-כָּל-הָאָרֶץ; בַּיּוֹם הַהוּא, יִהְיֶה יְהוָה אֶחָד--וּשְׁמוֹ אֶחָד.
The Lord will be king over all the earth; in that day will God be One, and His Name One.