Religion does not exist in a vacuum. Throughout history, proximity has caused cross-pollination of ideas and even symbols. Archaeologists have found symbols from Greek mythology in ancient Jewish temples. Several months of the Jewish lunar calendar are the names of Babylonian gods, such as Tammuz. Christianity, which certainly has its roots in Judaism, was also heavily influenced not only by the Greek language in which the New Testament was written, but by Greek philosophy, which the apostle Paul quoted widely. Christianity has also been influenced by the different cultures into which it has spread, including American culture.
Jewish-Christian relations today are somewhat dependent on where these relations are taking place. In the Middle East, where they have been relating to each other for a long time, some of the oldest Christian denominations still exist, and in many cases, though not all, the Jewish-Christian relationship is overshadowed by the Jewish-Arab one.
Another factor in Jewish-Christian relations is that Christianity has experienced cycles of philo and anti-Semitic thinking. In the earliest days of the Church there were so-called Judaizers who promoted circumcision and Jewish dietary restrictions. Martin Luther studied Hebrew with Rabbis and was very friendly toward the Jews until he became disappointed at their recalcitrance regarding conversion and wrote the tract, “Against the Jews and Their Lies,” which advocated the burning of synagogues and the expulsion of the Jews from Germany.
The Puritans and Separatists who settled New England were Hebrew scholars. One even named his son Maher-Shalal-Hash-Baz after the name that Isaiah was instructed to name his. The name literally means: “Hasten booty, hasten plunder,” not a very euphonious moniker.
A major factor influencing Jewish-Christian relations in the modern world was the Six Day War in 1967. This coincided with the Jesus Movement, a revival of non-denominational, some would say Primitive religion in the sense of a return to the roots. It has always been a challenge for a religion or movement born in a time steeped in End of the World apocolypticism to adjust to the continuing march of time. Two thousand years ago, Judaism itself was in an apocalyptic stage, facing national and religious collapse. Both faiths have had to reinvent themselves, as every system must do to survive in a changing world.
Every religion seems to go through a period of triumphalism. The Jewish zealots who barred the exits to the walled city of Jerusalem, expecting a God-given victory over the Roman empire, the Christian crusaders marching and riding into the unknown, expecting the restoration or foundation of a Christian empire based in the Holy Land, are just two examples of such triumphalism. Usually these triumphalist episodes are left behind, though they go in cycles too.
Israel's seeming miraculous victory over six Arab armies in six days in 1967 brought about a sense of euphoric pride among Jews, and a reevaluation of what became known as “Replacement Theology” among certain groups of Christians. For them, 1967 was a major event on the road to Armageddon, where all nations would be judged. Admittedly, many members of both religions are quick to admit that they don't have all the answers, and this is indeed a positive development, since, after all, humility is considered a virtue in each faith.