Think again, Peter was writing to the Jews in his letters. read the very first verse in 1 Peter
Peter, an apostle of Jesus Christ, To God’s elect, exiles scattered throughout the provinces of Pontus, Galatia, Cappadocia, Asia and Bithynia, 2 who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, to be obedient to Jesus Christ and sprinkled with his blood:
The elect in the NT always refers to Jews.
If that is not enough, you can also refer to Galatians 2:9
And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.