In the first epistle of Peter there are multiple statements that indicate that Peter’s thought process was quite different than that of modern day Zionism.
To begin with, Peter addresses his brethren as “aliens, scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia…” (1:1)
For the first century Jew, the diaspora wasn’t over, and yet the gospel proclaimed it was. For Christ had brought an end to the real exile, and now God was calling his people to an inheritance that is imperishable and undefiled and will not fade away, reserved in heaven for them ( v. 4).
The land under the law had served as a type of the true spiritual inheritance they would find in Christ.
In chapter one, he says the following in verses 14-19
As obedient children, do not be conformed to the passions of your former ignorance, but as he who called you is holy, you also be holy in all your conduct, since it is written, “You shall be holy, for I am holy.” And if you call on him as Father who judges impartially according to each one’s deeds, conduct yourselves with fear throughout the time of your exile, knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot ~ ESV
Now they were members of a new kind of Israel: a royal priesthood, and a holy nation, and chosen generation, called to offer up spiritual sacrifices by Jesus Christ (2:9).
Peter continues by addressing them as “strangers and pilgrims” (2:11), and encourages them to live in a way that honors God among the Gentiles in this world, as they follow Jesus Christ in anticipation of his glorious return.