If Jesus is the cornerstone, then the believers are the stones that are laid on the stone in order to build up a Temple. Peter compares the people of God to the stones that make up a “spiritual house.” If Jesus is like the chief cornerstone (in some ways like the foundation and in other ways like the capstone), then those who are in Christ are the other components of that building. This is not too far from Paul’s “body of Christ” metaphor, in which Christ is the head and believers are the members of the body.
There are several well-known critiques of the Temple, including the Temple Action by Jesus just before his crucifixion. Jesus called the activity around the Temple as a “den of thieves” and threatened to tear the Temple down and rebuild it in three days. We know now that he was talking about his body and the coming resurrection, but there were many who saw this as an attack on the Temple itself.
Stephen’s speech in Acts 7 is often seen as critical of the Temple and the aristocratic priesthood. Stephen claimed that there is simple no need for a “spiritual house” in the present age, and he was lynched for this attack! The Qumran community in particular considered the activity of the Temple to be corrupt. The community seems to have considered their activity near the Dead Sea as a kind of replacement for Temple worship until the Temple was cleansed by the coming messiah.
In the same way, the original readers would have understood “holy priesthood” in the light of the Temple. In fact, the priests were the only ones who permitted to offer sacrifices at the temple. Peter describes all believers as a “holy priesthood,: not just those members of the tribe of Levi or the family of Aaron. The high priest was to come from the line of Zadok, but after the Maccabean Revolt the Hasmoneans served as priest-kings, despite only being from the tribe of Levi. Since they were not Zadokites, the Qumran community rejected them proper high priests.
At the time this letter was written, the high priests were appointed to the office by the Sanhedrin. The high priest Ananus son of Ananus was removed from office in A.D. 63 because he executed James the brother of Jesus (Josephus, Antiq., 20.9.1). The high priest Joshua ben Gamla obtained the office in 64 after his wealthy wife bribed the right people; the final high priest, Phannias ben Samuel, was not even in the priestly line, but was appointed by the Zealots. Josephus said that he was a “mere rustic “and “a man not only unworthy of the high priesthood, but that did not well know what the high priesthood was.” (Josephus, JW, 4.151-158).
The believer is superior to the Temple priest because they are able to bring “acceptable sacrifice to God” because they are offering them “through Jesus.” Again, if there were some Jewish groups that considered the Temple and the priesthood corrupt, then can their sacrifices be acceptable to God? If, for example, the high priest was not actually holy when he brought the Day of Atonement sacrifice (on the wrong day even!), is it possible that God did not accept that sacrifice?
All of this language sounds like Peter is describing the present people of God as a kind of New Israel, but it is not the case that Peter is saying that the present Church (the Body of Christ) replaces the old Israel. For a Jewish writer and reader this new priesthood and temple service replaces the old one that was ineffective. The believers in Asia Minor in the first century are now all priests that are capable of offering acceptable sacrifices to God.