Does the concept of Gentile exist in Christianity?

In the Teachings of Jesus and the writings of the Apostles, there is a common theme of the world that represents an established system that is separate from and foreign to Messiah.

John 14:16-18 And I will ask the Father, and he will give you another co-minister, that he should abide with you into the ages: the Spirit of Truth, whom the world is not able to receive, because the world does not contemplate the Spirit or know the Spirit. But you know the Spirit, for the Spirit abides in you, and in you the Spirit will be. I will not leave you orphans, I am coming to you. Just a little while longer, and the world will not see me, but you will see me.

John 17:14 I have given your word to [the men you have given me], and the world detested them, because they are not of the world as I am not of the world.

John 14:27 I leave you with peace. I give you my own peace. I do not give to you like the world gives. Do not let your hearts be troubled.

John 14:30 No longer will I speak many things with you, for the one of the world is coming- the chief, and he does not have one thing in me.

This chief (αρχε "principle" or "foremost") of the world is also mentioned by Paul,

Ephesians 2:1-3 And you were dead in your trespasses and sins, in which at one time you walked according to the age of this world, according to the chief of the power of the air of the spirit of the one now working in the sons of disobedience.

John clarifies the spirit to which Paul refers in his own teaching on the world.

1 John 4:2-6 And every spirit that does not acknowledge Jesus Christ has come in the flesh is not of God, this is that of the antichrist, of which you have heard, 'it is coming', and now it is already in the world. You are from God, little children, and have overcome them; because greater is He who is in you than he who is in the world. They are from the world; therefore they speak as from the world, and the world listens to them. We are from God; he who knows God listens to us; he who is not from God does not listen to us. By this we know the spirit of truth and the spirit of error.

The world is a system which in the mind of the Christian is similar to the notion of Avoda Zarah among Jews. Avoda Zarah translates to "foreign worship" or "idolatry." In Romans, Paul equates men operating according to the spirit of error with idolaters,

Romans 1:18-23 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools, and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures.

"An image in the form of corruptible man and of birds and four-footed animals and crawling creatures" is an idol. Paul continues speaking of those who suppress the truth,

Romans 1:24-25 Therefore God gave them over in the lusts of their hearts to impurity, so that their bodies would be dishonored among them. For they exchanged the truth of God for a lie, and worshiped and served the creature rather than the Creator, who is blessed forever. Amen.

These men who operate according to the spirit of the world, the spirit of error, are then by definition idolaters, which is Avoda Zarah. Those who teach lies according to the spirit that is in the world are antichrists, which translates literally from the Greek to the counter-anointed.

1 John 2:18-19 Children, it is the last hour. You heard that the antichrist is coming, even now many antichrists exist. This is how we know that it is the last hour. They went out from us, but they were not of us; for if they had been of us, they would have abided with us; but this happened so that it would be apparent that not all are of us.

The world has no part in Messiah or in the Kingdom of God, because the world rejects and hates the things of God. This is how Christians are taught to see the world in practice:

1 John 2:15 Do not love the world, or the things of the world! If anyone loves the world, the love of the Father is not in him, because every thing in the world- the desire of the flesh, the desire of the eyes, and the vanity of living- is not of the Father, but is of the world.

No.

In Christianity, there are two sets of people, but one group is not excluded or held to different standards than the other. There are:

1. God's chosen covenant people.
2. Everybody else.

God's people are identified solely by their faith in Jesus Christ as savior/redeemer. By faith we become part of the same family. With those who have faith in His Son, God had made an everlasting covenant to bring them into His kingdom as join heirs with Christ himself.

Everybody else can be labeled however you like (e.g. pagans, non-Christians) but it all boils down to the same thing. The "rules" that apply to them are simple:

Acts 16:31 (ESV)
³¹  […] “Believe in the Lord Jesus, and you will be saved, you and your household.”

Most branches of Christianity see Jesus, the Son of God, as the Jewish Messiah in fulfillment of Jewish prophecies and foreshadowing in the Jewish Scriptures.

God foretold, though, that the Seed of Abraham would be a blessing to all people--every tribe, tongue and nation. The apostle Paul specifies that the gospel is to the Jew first and also to the Gentile.

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 *[Gentile]*. Romans 1:16 ESV

Jesus was born to a Jewish mother in a Jewish city in the land of the Jews. His first followers were Jews and the earliest growth of the church was among Jews (Acts 1-7).

So, non-Jewish believers in Jesus identify themselves as the Gentiles--the ones who were once "outside" but who are now "included". We see ourselves as the "other sheep" of which Jesus spoke when He was addressing a Jewish audience.

And I have other sheep that are not of this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd. John 10:16 ESV

Messianic Jews--Jews who recognize Jesus as their Messiah--oftentimes consider themselves "completed Jews", or Jews that recognize the Messiah that God foretold and sent into the world.

So, in conclusion, non-Jewish Christians see themselves as the Gentiles that God blessed through Jesus, who is both the God of Abraham and the descendant of Abraham in the flesh.

The term Gentile in the Bible simply means non-Jew or non-Hebrew. In Old Testament times, the Hebrews called the other non-Hebrews as Gentiles and in the New Testament, non-Jews are Gentiles.

In the New Testament, Paul was famous for preaching to the Gentiles. Because Paul was a Jew, he was zealous for his own people and preached the gospel mostly to the Jews first. But later, as his own people rejected him, his focus shifted towards the Gentiles.

Romans 10:1 (NIV) Brothers and sisters, my heart’s desire and prayer to God for the Israelites is that they may be saved.

Acts 18:5-6 (NIV) When Silas and Timothy came from Macedonia, Paul devoted himself exclusively to preaching, testifying to the Jews that Jesus was the Messiah. But when they opposed Paul and became abusive, he shook out his clothes in protest and said to them, “Your blood be on your own heads! I am innocent of it. From now on I will go to the Gentiles.”

Romans 11:11 (NIV) Again I ask: Did they stumble so as to fall beyond recovery? Not at all! Rather, because of their transgression, salvation has come to the Gentiles to make Israel envious.

According to New Testament, anyone who is not a Jew is a Gentile, whether he is a Christian or not. And believe it or not, most of the users in this site are Gentile Christians.

Some recent new Christian sects call all non-Christians including Jews as Gentiles but it's not biblical. All non-Jews are Gentiles but non-Jews who are non-Christians are more appropriate to be referred to as Pagans, Heathens, Infidels or simply non-believers, depending on the target.