Dispensationalists caricature the historic orthodox position of the Church as "replacement" or "supercessionist" theology, but as one looks through Scriptures, it's actually neither. In fact, it's a theology of the fulfilment of the covenant. The Scriptures are divided into two parts: the Old Testament and the New Testament. But the word "Testament" is generally criticized as a bad translation. The more accurate translation, and what is more revealing, is "Covenant". In Genesis, God made a covenant with Abraham (Gen. 15-17). At the Last Supper, Jesus declared that what His Apostles were drinking was "the Blood of the New Covenant" (Matt. 26:28). Everything in Scripture about God's relationship with humanity centers around the idea of covenants. God makes multiple covenants in Genesis with Noah and with Abraham, and then He becomes a man and makes a New Covenant with the shedding of His own Blood. The Covenant establishes His bond with His people.
When He makes a covenant with Abraham, He promises that Abram will be a father of many descendants and describes the boundaries of their lands, that his descendants will number the stars of the Heavens, and that they will be held in captivity for four hundred years (Gen. 15:4-21). Then, God changes the name of Abram to Abraham and declares that Abraham will be the father of many nations (Gen. 17:7). Abraham is not to be the father of one nation only, but of multiple nations. We can see that there are many peoples throughout the world who confess the name of Christ. God foreshadows an everlasting covenant to be made with the descendants of Abraham. This is not just referring to one nation of Israel or one specific group of people. God's intentions, from the beginning, with Abraham, was to use the descendants of Abraham according to the flesh, to be a light for the whole world.
There are multiple instances where "Israel" is referred to in Scriptures. It is referred to in Scriptures as Jacob the Righteous, the son of Isaac. It is referred to in Scriptures as the Kingdom of Israel. It is referred to in Scriptures as the people of Israel, the people of the Kingdom of Israel. Even dispensationalists have to acknowledge that the modern State of Israel is not a Kingdom but a democratic parliamentary republic. But there are already is a King of Israel according to Scriptures! In the Davidic line of descent, the Messiah is born to the Virgin Mary and becomes King of Israel! Moreover, it is revealed in the fulfilment, that this King was to come, not just to the Hebrews but to all nations. Such was the mission work of Christ. He clarifies that He has come for the Hebrews first, but with full intention to incorporate the Gentiles. This became an early question for the Church (Acts 15:3-21). In this controversy over the question of the circumcision of the Gentiles, the Holy Prophet Amos is referenced, "I will raise up the tabernacle of David, which has fallen down ... [a]nd all the Gentiles who are called by name" (Am. 9:11-12).
So even in the Old Covenant, it is explained that Gentiles were to be included in the promises of Israel! As St. Paul declares, "Now to Abraham and his Seed [Christ] were the promises made" (Gal. 3:16). Those who are included in the promise are of Israel, the Seed of Israel, because Christ is the firstfruits of Resurrection (1 Cor. 15:20). Christ has established Himself as firstborn of a brotherhood and this includes those who find Faith in Christ. Christ establishes Himself as King over all nations in the glory of His Resurrection and the splendor of His Godhood. The Kingdom of Israel, therefore, must be the Church. But St. Paul also recognizes that there is a remnant of Israel according to the flesh.
In Romans 9-11, where many dispensationalists come away with the understanding that their opponents' theology is somehow a "replacement" theology, they miss on key concepts that St. Paul speaks of the remnant of Israel (Rom. 9:27-28). The point is to show that Abraham has descendants according to the flesh, but that the flesh will account for nothing in the judgment from God. Much the same, even Jesus makes note of this in His dispute with the Pharisees where He declares that they are not the children of Abraham but of the Devil (Jn. 8:44). St. Paul is much aware of the statements made by Christ and is making an argument showing that the Gentiles are indeed apart of the Covenant, but how the Covenant is not superceded at all. Ironic that fulfilment theology is often termed "supercessionist" because it is anything but!
When I went to a non-denominational church when I was younger, the pastor once informed us that Paul was a "Jew" and emphasized in his lecture the Jewishness of Paul. I was both disturbed and perplexed. This is because the distinguishing of Judaism and Christianity as a religion nor the ethnic distinction was actually applied. But if we look at Scriptures, we do come across the statements made by St. John that there are Jews who say they are Jews but are of the Synagogue of Satan (Rev. 2:9, 3:9). It is not the replacement of Israel that we are looking at in Scriptures, but the fulfilment of Israel. The writers of the Catholic epistles want us to come away with the understanding that we are indeed correctly called Israel, have the promises of Israel, and are included in that. They cite the Old Testament's references that include the Gentiles in that Covenant and show the intent to incorporate the Gentiles into that Covenant. The Gentiles are restored with the tabernacle of David. That is the Church. Anything that contradicts is actually supercessionist and replacement. Was St. Paul a "Jew"? He was a Jew who was a Jew in reality. But that is because the true Jewish religion is not that of Rabbinic Judaism, but that of the Messianic following of Christ in the Sacrament of the Blessed Eucharist. Both "Christian" and "Jew" is appropriate for Christians are Jews of the New Covenant. Those tied to the Old Covenant stand in rejection of Christ. They deny that Christ came in the flesh and are Antichrist (1 Jn. 2:22, 4:3; 2 Jn. 1:7). Thus, St. John distinguishes between Jews who are of the Synagogue of Satan and practitioners of the true Faith (called Christians).
The word "Christian" was first applied to those who followed Christ as the Messiah by the opponents of Christianity and not by Christians themselves. The first Christians more than likely would have viewed themselves as a sect of Judaism at the time. When we sort through the anachronisms, and understand the texts according to the way the early Christians saw it, we see that they viewed Jewishness far differently than it is understood nowadays, Israel is a Kingdom of which the Church (Ekklesia - gathering) is the standing army, and the Eucharist is the sacrifice. Because many Protestants have rejected that the Eucharist is sacrifice and that Jesus's pouring Himself out on the Cross once and for all is infinitely offered on the Holy Altars, they miss out on this. That's how dispensationalism is arrived at. Because Lutherans and Anglicans haven't dismissed that theology of the Eucharist, they have retained the same views as historic Christianity. Dispensationalism is, effectively, replacement theology because it throws the Gentiles out of the Covenant and replaces the Kingdom of Israel with the modern State of Israel. Dispensationalism, therefore, is heretical.