This is a favourite passage for those who teach Replacement Theology. They teach that what the Old Testament stated to be true of Israel, Peter now applies and states to be true of the Church. Thus, they conclude that the Church has replaced Israel. However, there is no hint in the epistle that Peter is addressing the Church as a whole. On the contrary, in the epistle’s introduction (1:1–2), he stated that he was addressing Jewish believers who specifically comprised what was the then Remnant of Israel—the Israel of God.
1 Peter1:1-2 – Peter uses three terms to describe the recipients of his letter. First, they are the elect, meaning they were chosen by God. This is a fact he highlights in 2:6, 9. Second, they are sojourners. The Greek word for sojourners is used only three times: here, in 2:11, and in Hebrews 11:13. It is a Greek word meaning “alien nationality” and “temporary resident.” As Jewish believers living outside the Land and living alongside pagan Gentiles, these sojourners were considered to be resident aliens. Thus, the term sojourners describe their relationship to the world. Third, the recipients are of the Dispersion. The word Dispersion remains a technical Jewish term to this day and refers to Jews living outside the Land. This word is used twice elsewhere: John 7:35 and James 1:1. In this case, the reference is not to all Jews but to only those Jewish believers dwelling outside the Land. They are twice distinguished from the Gentiles among whom they live (2:12 and 4:3).
So, it is important to recognize that the contrast Peter makes here is not between the Church and Israel, or between believers and non-believers, or between unbelieving Jews and believing Gentiles. Rather, the contrast here is between the Remnant and the Non-Remnant of Israel. Peter’s point is that while Israel the whole failed to fulfill its calling, the Remnant of Israel has not failed to fulfill its calling.
Arnold G Fruchtenbaum, Ariel's Bible Commentary: Messianic Jewish Epistles (San Antonio, TX: Ariel Ministries, 2005) pp. 318-319; 344