It was interesting because one time, I was having a conversation with my חַזָּן about the Israeli-Palestinian conflict. He told me, "You want to know when it [the conflict] began? It wasn't with the creation of the state of Israel. It goes back to Yishmael and Yitzchak (Isaac)." When I was initially told that, it took me aback to think that such a conflict goes all the way back to the book of Genesis. But after looking at the Jewish texts, it makes sense. What one has to keep in mind is that Muslims can trace their ancestry back to Yishmael, just as the Jewish people trace theirs back to Yitzchak.
A few important things that can be said about Yishmael. In Genesis 21:20, we read that Yishmael was an accomplished archer. There is a Midrash (Pirkei D’Rabbi Eliezer, ch. 30) that expounds upon that by telling us that Yishmael was born with a bow, meaning that bloodshed does not merely come from training, but is something innate. Other texts illustrate this by saying that he got this from his mother, Hagar, who wanted to be free from the restraints of civilization (Bereishit Rabbah 45:9, Sforno on Bereishit Rabbah 16:6,8).
When reading about the covenant with Ishmael in the book of Genesis, we see that G-d promises a few things: that his descendants will be one great (not necessarily good) nation (17:20), but more importantly, that he will be antagonistic to everyone, including his brothers (16:12). It is worth noting that the phrase used to describe Yishmael is פֶּרֶא אָדָם, which is best translated as an uncivilized man. R. Samson Hirsch explains that פֶּרֶא אָדָם denotes a man liberated from the confines of social order. “His hand against everyone” means that Ishmael removes himself from the laws of society. As he sets about fulfilling his wishes at any cost, chaos ensues (ibid). Even the Chofetz Chayim (Peninim MiShulchan Gavoha on Berishit, p. 78) had the following to say about Yishmael, the פֶּרֶא אָדָם:
The Torah is eternal. When the Torah tells us that Yishmael is a פֶּרֶא אָדָם, it means that he will remain that way forever. Therefore, any attempt by the "cultured" nations of the world to civilize him will be unsuccessful because Yishmael is uncivilized. Woe, who knows what this פֶּרֶא אָדָם is yet likely to do to the Jewish nation at the end of days.
Looking at the Jewish texts, it seems to be stating that any pre-Messianic attempt to "give peace a chance" is futile, not to mention that it has thus far predicted the overall friction between the two religions.
Although the conflict between Yishmael and Yitzchak goes back way before the creation of the religion of Islam, it definitely gives some context of what ensues within the life of Mohammed. To make a long story short, Mohammed was a merchant, but one day, he allegedly was given divine revelation in a cave by the Angel Gabriel. He then felt the need to deliver his version of monotheism to the world. During his travels, he had come across many Christians and Jews, but he had particularly been inspired by the Jews. That is why prayer was in the direction of Jerusalem and he kept kashrut, amongst other Jewish rituals. His admiration for Judaism, however, dissipated when the great majority of Jews rejected his "Arab version of Judaism," and rightly so. The result--Mohammed's animosity. He changed the direction of prayer to be towards Mecca rather than Jeruslaem. Short of the prohibition on the consumption of blood and pork, he did away with kashrut. And he also did away with the Sabbath being the holiest day of the week and moved it to Friday. His animosity was coupled with the fact that he had eventually gained enough momentum by 622 CE to acquire a military force.
Before continuing, I have to make a note of how certain things are abrogated (abrogation is based on the Qu'ran 2:106) in the Qu'ran. When reading the Qu'ran, one has to realize that the book is not in chronological order. Although there is some dispute as to the exact chronological order, one thing I have found is that Sura 5 and Sura 9, the chapters describing Jews and Christians in a negative fashion, as well as the infamous verse, 9:29, describing an external, global jihad with unbelievers, are chronologically at the end of Mohammed's "revelation." This means that any peaceful verses one would find from Mohammed's earlier days would have been abrogated by his violent ones. Even if one rejects the Qu'ran as divine, the progression of his hatred towards the unbeliever makes sense. As more Jews [and Christians] reject his version of monotheism, he becomes more embittered by their denial of Mohammed. As his army grows, he is able to better exhibit his anger because he doesn't have to play nice anymore.
Mohammed's view of the kafir, the unbeliever, has to make us pause. In the Qu'ran, it is said that a kafir is an antagonist (3:28), ignorant (6:111), untrustworthy (5:54), arrogant (35:42-43, 40:76), a liar (51:9-10), disgraced (37:18), meriting of punishment (2:88, 68:44), a partner of Satan (2:168-169, 25:55), unclean (9:28), and as a result, will burn in hell (98:6). Because the kafir is "so despised in the 'eyes of Allah'," the kafir can be hated (40:35), enslaved (Bukhari 5,58,148), raped (Ishaq 759), mocked (83:34), punished (25:77), beheaded (47:4), plotted against (86:15), terrorized (8:12), killed (4:91, 6:45), crucified (5:33), faught in jihad (9:29), and humiliated, most notably via a jizya, which is a burdensome poll tax (ibid). When going through the Qu'ran, approximately 94% of all references of "going to Hell" say that you merit it because you disagree with Mohammed, which means that being Jewish doesn't make you "O.K. with Allah." Talk about reassuring....
Even if you decide to ignore that these verses exist or that they have been taken out of context, it cannot be denied that these verses have been used to treat the non-believer horribly throughout history. When the Muslims conquered a given land, they gave the "People of the Book" three options: die, convert, or be given status of dhimmi. For those who don't know what dhimmi status is, it is a subservient pact that allows a non-believer to live in a Muslim world as a non-believer. This pact, however, came with many humiliating provisions. For instance, one had to pay the jizya. Distinctive clothing, most notably a yellow badge, had to be worn. A Jew was not permitted to have a synagogue could ever be higher than a mosque, not to mention that they could ever build new synagogues. A Jew could never give evidence in a Muslim court. A Jew could not inherit from a Muslim. A Jew did not have a right to bear arms. These are just some restrictions placed on the Jew, as well as the Christian. Although all prohibitions were not applied equally or universally, it is safe to say that the typical Muslim believed that the Jew [and the Christian] was inferior to the Muslim. Even though this view should have died along with the Middle Ages, it still unfortunately permeates in the minds of many Muslims.
Conclusion: This treatise was written to better understand the origin of Judeo-Muslim tension. As for any attempt to ameliorate the conflict between the two religions, I guess we'll have to save that discussion for another time.