The previous post re:Israel and the Church should be understood from the right perspective and we trust that this was reasonably clear. There are three main perspectives in relation to Israel and the Church.
1) Replacement Theology. This perspective teaches that the Church replaces Israel. Charles D. Provan's title "The Church is Israel Now" may not intend to signify this but it is certainly unfortunate and not a phraseology to be used. Replacement Theology (sometimes called Supercessionism) was taken to its very unpleasant anti-Semitic extreme in medieval Roman Catholicism. This perspective asserts that the Church exactly replaces Israel, so that the latter is always to be read into the Old Testament as the replacement of the former.
2)Repudiation theology. The perspective that repudiates any connection between Israel and the Church. It is a view classically espoused by Dispensationalism which views the Church as a mystery which is unmentioned and unknown in Old Testament Times. According to this view it is a parenthesis required as a contingency plan because Israel rejected Christ as Messiah. The prophetic time-clock for Israel has therefore been paused at this point but will resume because the Mosaic covenant with Israel is intended to be permanent. Interestingly Romanism has now shifted to the idea that this covenant is permanent and the Jews are saved in their own way.
3) Reform Theology. The third perspective is that the Church represents an extension of Israel because there is only one overall people of God and one overall covenant. This is the view of covenant theology. The Church is the reform or renewal of Israel. The New Covenant extends what was already present in the Old Covenant. Hebrews 9:9-11 identifies the New Testament era as the time of reformation in speaking of the tabernacle and its ceremonial ordinances:
"Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation. But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building"
These perspectives have a connection with eschatology. Replacement theology is seen in classical A-Millennialism of the pessimistic variety. Augustine espoused this view. Consistent A-Millennialists see no role for ethnic Israel and no unfulfilled prophecy related to them. OT prophecy is exclusively interpreted as fulfilled in the Gentile Church. Preterism especially full-preterism has a tendency to replacement theology. The only exception is where partial preterism may join with the optimistic A-Millennial in expecting a conversion of the Jews.
The repudiation of a connection between Israel and the Church is, as mentioned, connected to Dispensationalism and similar types of premillennialism.
Postmillenialism is the most consistent application of Reform theology in that it sees a role for ethnic Israel in being brought back to its olive tree and Israel blossoming and budding and filling the face of the earth with fruit.
There is also an ecclesiological aspect to these perspectives.
Roman Catholicism (and Episcopalianism to an extent)is an express imitation of the ceremonial forms of Israel with its sacrificing priesthood and festivals. Erastianism assumes that the Church should be governed as Israel was with a monarch at its head, according to an erroneous interpretation.
Repudiation between Israel and the Church is applied in areas of Church Government and practice such as baptism rejecting the application of the seal of the covenant to children and the sabbath, in some cases rejecting the abiding principle of the sabbath. It says that unless something is expressly commanded in the New Testament it is no longer applicable to the Church.
The reform view of Israel and the Church sees continuity and extension of the principles established in Israel's church government but does not see the ceremonial ordinances only imposed until the time of reformation as permanent. What has not been abrogated continues. This is the view upheld by presbyterianism.
It should be recognised that individuals are more or less consistent in applying these things. Thus there are amillennialist presbyterians and postmillennial baptists. Nevertheless the broad observations obtain.