Peter was writing to scattered Jews 1Peter 1:1If you read the first chapter of 1 Peter, it's clear that he is talking to believers. I don't see anything in chapter 1 indicating that Peter is only addressing believers who are descendants of Israel.
In chapter 2, Peter is contrasting Israel who rejected Jesus as the Messiah--"the stone that the builders rejected" to believers, who accept Jesus as the Messiah. He says "but YOU [believers] are a chosen race, a royal priesthood,...." Peter makes no indication that he is not addressing all believers.
1 Peter 2
So rid yourselves of all malice, all deceit, hypocrisy, envy, and all slander. Like newborn infants, desire the pure spiritual milk, so that you may grow by it for your salvation, since you have tasted that the Lord is good. Coming to Him, a living stone — rejected by men but chosen and valuable to God — you yourselves, as living stones, are being built into a spiritual house for a holy priesthood to offer spiritual sacrifices acceptable to God through Jesus Christ.
For it is contained in Scripture:
Look! I lay a stone in Zion,
a chosen and honored cornerstone,
and the one who believes in Him
will never be put to shame!
So honor will come to you who believe, but for the unbelieving,
The stone that the builders rejected —
this One has become the cornerstone,
and
A stone to stumble over,
and a rock to trip over.
They stumble because they disobey the message; they were destined for this.
But you are a chosen race, a royal priesthood,
a holy nation, a people for His possession,
so that you may proclaim the praises
of the One who called you out of darkness
into His marvelous light.
Once you were not a people,
but now you are God’s people;
you had not received mercy,
but now you have received mercy.
Peter spoke of them as a holy nation and priests just as God spoke of concerning Israel Exodus 19:6