Saint John Paul II
Some sources such as Wikipedia record the pope as believing in dual covenant theology. The problem with this is there is no back-up source. In fact there are articles devoted to debunking this assertion and he himself made it clear that he did not espouse such a doctrine. Dr. Robert Sungenis for example defending the pope’s stance on the Covenant.
Saint John Paul II said it short and straight to the point: “Christ fulfills the divine promise and supersedes the old law” . This is more like replacement theology or supercessionism than dual covenant theology. While he did admit to the importance of the Old Covenant as God’s promise . Other quotes he made which obviously do not sound like dual covenant theology are the following.
“The Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism, …” (CCC 676)
“He therefore chose the Israelite race to be his own people and established a covenant with it. He gradually instructed this people…. All these things, however, happened as a preparation for and figure of that new and perfect covenant which was to be ratified in Christ… the New Covenant in his blood; he called together a race made up of Jews and Gentiles which would be one, not according to the flesh, but in the Spirit.” (CCC 781)
“When she delves into her own mystery, the Church, the People of God in the New Covenant, discovers her link with the Jewish People, …” (CCC 839)
“Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.” (CCC 846)
“The Old Law is the first stage of revealed Law.” (CCC 1962)
“According to Christian tradition, the Law is holy, spiritual, and good, yet still imperfect.” (CCC 1963)
“In any case, even though the Old Law prescribed charity, it did not give the Holy Spirit, …” (CCC 1964)
“The Law of the Gospel fulfills and surpasses the Old Law and brings it to perfection: …” (CCC 1984)
Supercessionism is itself a biblical doctrine. Scripture repeatedly speaks of the New Law fulfilling the Old, how believing Jews and Gentiles are the Church, the New Israel. This has been maintained through Sacred Tradition and to this day the Church teaches it. It is necessary to be baptized by water, blood or desire in order to be saved and the Second Vatican Council upheld this doctrine . Some self-styled traditionalists unfairly accuse the pope of rebuking Church doctrine and as shown such accusations are nonsense.
 Saint John Paul II. Redemptoris Mater, footnote 2.
 Catechism of the Catholic Church, n. 709
 Lumen Gentium, n. 14; Ad Gentes, n. 7