Tension between Judaism and Christianity goes back to the generation of Jesus and the Apostles. John the Baptist was accepted as a prophet by the followers of Christ, but rejected by the official leadership of Judaism in Jerusalem. Likewise, Jesus himself, although like John receiving support from the masses, was rejected by all but a few in the hierarchy of Judaism, a group that was the focus of much of Jesus' ire in his preaching. In the Early Church, first centered in Jerusalem under the leadership of Jesus' half-brother James, and peopled almost entirely by converts from Judaism (who considered themselves to be reformers of Judaism, not founders of a new religion), there was also tension with the leadership of Judaism which led to the first Christian martyr after Jesus: Stephen.
The Early Church might have retained a strong connection to Judaism if not for two later developments: the massive success of the Apostle Paul among Gentiles (and concurrent failure among his own people, leading to the anguished thoughts of Romans 9-11, excerpted below), and the destruction of Jerusalem leading to the end of 2nd Temple Judaism and the Diaspora. As the first generation of the Church came to a close, the organization took on a distinctly Gentile character, and its Jewish origins faded into the background.
Animosity and hostility toward the Jewish minority in what was to become Christendom was not non-existent, but it was never widespread on the level that would become the later pogroms, forced conversions by the Inquisition, and then ultimately genocide at the hands of the Nazis until the Late Middle Ages. In 1096, in response to Pope Urban II's call for a Crusade to recapture the Holy Land, Peter the Hermit, who raised an army in the Rhineland, perpetuated there the first large scale massacre of Jews by Christians. To the shame of the Church, this trend has continued to this day, and while few are alive who witnessed the Holocaust, the scourge of Antisemitism residing within those claiming to be a part of the Church remains.
This is, of course, a patent absurdity. There is no such thing as Christian Antisemitism. There are those who claim to be Christian who espouse Antisemitism, and there may be those who are indeed Christians whose minds are still infected with Antisemitism, but the two mindsets are diametrically opposed to each other. In the end, the mind of Christ will prevail, and hate will be banished, or the true un-regenerated nature of those claiming to follow Christ will be revealed and their ongoing hatred will refute any pretense of being a Christ-follower.
There is, and must be, a gap between Christianity and Judaism (as long as one accepts and the other rejects Jesus as the Messiah), but that gap ought to elicit sorrow and compassion on the part of Christians, as it did for the Apostle Paul, and not prejudice or hatred. We have, as Christians, an undeniable debt toward Judaism, for our New Covenant and New Testament are built upon the Abrahamic/Mosaic Covenant and the Hebrew Scriptures.
It is incumbent upon Christians, always and everywhere, not as an option but an obligation, to reject Antisemitism in both its violent forms and its more subtle conspiracy theories and racial stereotypes, those who fail to do so are doing a disservice to the Gospel, and those who instead embrace them by their attitudes/words/actions are declaring themselves to be fighting against the Word of God, and calling into question their own salvation.
That the Church has failed to live up to the demands of Scripture by allowing Antisemitism to fester and even thrive in its midst, and that the people associated with the Church have been either bystanders to, or complicit in, the brutalization of the Jewish people and eventually their genocide, is the greatest shame and most enduring stain upon the Bride of Christ. We, collectively, over the past 2,000 years, have failed in this, we will answer to God for that failure, for Christian Antisemitism is an abomination.
Romans 9:3-5 New International Version (NIV)
3 For I could wish that I myself were cursed and cut off from Christ for the sake of my people, those of my own race, 4 the people of Israel. Theirs is the adoption to sonship; theirs the divine glory, the covenants, the receiving of the law, the temple worship and the promises. 5 Theirs are the patriarchs, and from them is traced the human ancestry of the Messiah, who is God over all, forever praised! Amen.
Romans 11:1-6 New International Version (NIV)
11 I ask then: Did God reject his people? By no means! I am an Israelite myself, a descendant of Abraham, from the tribe of Benjamin. 2 God did not reject his people, whom he foreknew. Don’t you know what Scripture says in the passage about Elijah—how he appealed to God against Israel: 3 “Lord, they have killed your prophets and torn down your altars; I am the only one left, and they are trying to kill me”? 4 And what was God’s answer to him? “I have reserved for myself seven thousand who have not bowed the knee to Baal.” 5 So too, at the present time there is a remnant chosen by grace. 6 And if by grace, then it cannot be based on works; if it were, grace would no longer be grace.
Romans 11:11-24 New International Version (NIV)
11 Again I ask: Did they stumble so as to fall beyond recovery? Not at all! Rather, because of their transgression, salvation has come to the Gentiles to make Israel envious. 12 But if their transgression means riches for the world, and their loss means riches for the Gentiles, how much greater riches will their full inclusion bring!
13 I am talking to you Gentiles. Inasmuch as I am the apostle to the Gentiles, I take pride in my ministry 14 in the hope that I may somehow arouse my own people to envy and save some of them. 15 For if their rejection brought reconciliation to the world, what will their acceptance be but life from the dead? 16 If the part of the dough offered as firstfruits is holy, then the whole batch is holy; if the root is holy, so are the branches.
17 If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, 18 do not consider yourself to be superior to those other branches. If you do, consider this: You do not support the root, but the root supports you. 19 You will say then, “Branches were broken off so that I could be grafted in.” 20 Granted. But they were broken off because of unbelief, and you stand by faith. Do not be arrogant, but tremble. 21 For if God did not spare the natural branches, he will not spare you either.
22 Consider therefore the kindness and sternness of God: sternness to those who fell, but kindness to you, provided that you continue in his kindness. Otherwise, you also will be cut off. 23 And if they do not persist in unbelief, they will be grafted in, for God is able to graft them in again. 24 After all, if you were cut out of an olive tree that is wild by nature, and contrary to nature were grafted into a cultivated olive tree, how much more readily will these, the natural branches, be grafted into their own olive tree!