Hebrews 8-9 are theologically more controversial than the rest of Hebrews because it appears that the writer of Hebrews says that the Jewish people have been replaced by the Church – the New Covenant has replaced the Old, Jesus’ sacrifice is superior to the old sacrifice. As such, chapters 8 and 9 have been used to teach that the Jewish people are no longer God’s people and the church replaces them completely. This would therefore imply that any promises made to Israel in the Hebrew Bible are either canceled or to be reinterpreted as applying to the Church.
The theological term for this is supersessionism, the church supersedes the Jews as the people of God. For some types of theology, the idea that the Jews have been replaced by the church is an assumption, the proof for which is found here in Hebrews, especially chapters 8-9. The historic view of the church is that it is the new Israel, and all the promises of the Hebrew Bible are fulfilled in the church. The rebuilding of Jerusalem mentioned in the New Covenant passage is therefore re-interpreted spiritually. For example, commenting Jeremiah 31,
The “wall great and high” is of no earthly material; the extension is not one of yards on miles, but of nations and ages; the consecration of the unclean places is but typical of the regenerative force of Christianity, which reclaims the moral wastes of the world, and purifies the carnal affections and sinful tendencies of human nature; and no material city could ever “stand for aye.” Only the kingdom and Church of Christ could satisfy the conditions of such a prophecy. (A. F. Muir, in The Pulpit Commentary: Jeremiah 2:28).
However, when one reads Hebrews without the modern church in mind, the book does not argue that Israel has been replaced, but that the promises made to Israel, including the New Covenant, have their fulfillment in Jesus the Messiah. I find Richard Hays, “We Have No Lasting City,” pages 151-173 in The Epistle to the Hebrews and Christian Theology (Grand Rapids: Eerdmans, 2009) to be an extremely helpful sketch of the problem. Hays cites his own work as implying that Hebrews is supersessionist, and then shows how a proper reading of Hebrews will show that the book is not actually teaching that the church has replaced Israel.