Christians who were formally Jews but in Christ there are no Jews or Gentiles.
1:3 Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead,
He uses the term Gentile to indicate someone who is not a child of God. Under the old law you had God's people (Jews) and those who were not (Gentiles). So today we have God's people (Christians) and those who are not (everyone else).
Here are some verses in the Bible (Christian New Testament) that refer to "Jew" or "Jews". There is nothing wrong with being a Jew. (All of these references are found after the book of Acts.)
Romans 1:16 NASB - 16 For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.
Romans 2:9-10, 17, 28-29 NASB - 9 There will be tribulation and distress for every soul of man who does evil, of the Jew first and also of the Greek, 10 but glory and honor and peace to everyone who does good, to the Jew first and also to the Greek. ... 17 But if you bear the name "Jew" and rely upon the Law and boast in God, ... 28 For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh. 29 But he is a Jew who is one inwardly; and circumcision is that which is of the heart, by the Spirit, not by the letter; and his praise is not from men, but from God.
Romans 3:1 NASB - 1 Then what advantage has the Jew? Or what is the benefit of circumcision?
Romans 10:12 NASB - 12 For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him;
1 Corinthians 9:20 NASB - 20 To the Jews I became as a Jew, so that I might win Jews; to those who are under the Law, as under the Law though not being myself under the Law, so that I might win those who are under the Law;
Galatians 2:14 NASB - 14 But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, "If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?
Galatians 3:28 NASB - 28 There is neither Jew nor Greek, there is neither slave nor free man, there is neither male nor female; for you are all one in Christ Jesus.
Colossians 3:11 NASB - 11 a renewal in which there is no distinction between Greek and Jew, circumcised and uncircumcised, barbarian, Scythian, slave and freeman, but Christ is all, and in all.
Romans 3:9, 29 NASB - 9 What then? Are we better than they? Not at all; for we have already charged that both Jews and Greeks are all under sin; ... 29 Or is God the God of Jews only? Is He not the God of Gentiles also? Yes, of Gentiles also,
Romans 9:24 NASB - 24 even us, whom He also called, not from among Jews only, but also from among Gentiles.
1 Corinthians 1:22-24 NASB - 22 For indeed Jews ask for signs and Greeks search for wisdom; 23 but we preach Christ crucified, to Jews a stumbling block and to Gentiles foolishness, 24 but to those who are the called, both Jews and Greeks, Christ the power of God and the wisdom of God.
1 Corinthians 9:20 NASB - 20 To the Jews I became as a Jew, so that I might win Jews; to those who are under the Law, as under the Law though not being myself under the Law, so that I might win those who are under the Law;
1 Corinthians 10:32 NASB - 32 Give no offense either to Jews or to Greeks or to the church of God;
1 Corinthians 12:13 NASB - 13 For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.
2 Corinthians 11:24 NASB - 24 Five times I received from the Jews thirty-nine lashes.
Galatians 2:13-15 NASB - 13 The rest of the Jews joined him in hypocrisy, with the result that even Barnabas was carried away by their hypocrisy. 14 But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, "If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?
15 "We are Jews by nature and not sinners from among the Gentiles;
1 Thessalonians 2:14 NASB - 14 For you, brethren, became imitators of the churches of God in Christ Jesus that are in Judea, for you also endured the same sufferings at the hands of your own countrymen, even as they did from the Jews,
Revelation 2:9 NASB - 9 'I know your tribulation and your poverty (but you are rich), and the blasphemy by those who say they are Jews and are not, but are a synagogue of Satan.
Revelation 3:9 NASB - 9 'Behold, I will cause those of the synagogue of Satan, who say that they are Jews and are not, but lie--I will make them come and bow down at your feet, and make them know that I have loved you.