The Church of Jesus Christ is every person that has believed on Him and followed Him by being baptized, thus declaring themselves to be followers of the Christ. In Christ it matters not whether you are Jew or Gentile, rich or poor, free or slave, male or female, black or white, green or orange, striped or polka-dotted, we are all ONE in Christ's Church.

Eph. 3:14-21

[14] For this cause I bow my knees unto the Father of our Lord Jesus Christ,
[15] Of whom the whole family in heaven and earth is named,
[16] That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man;
[17] That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love,
[18] May be able to comprehend with all saints what is the breadth, and length, and depth, and height;
[19] And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God.
[20] Now unto him that is able to do exceeding abundantly above all that we ask or think, according to the power that worketh in us,
[21] Unto him be glory in the church by Christ Jesus throughout all ages, world without end. Amen.

1 Cor. 10:31-32

[31] Whether therefore ye eat, or drink, or whatsoever ye do, do all to the glory of God.
[32] Give none offence, neither to the Jews, nor to the Gentiles, nor to the church of God:

God's plan for the New Covenant was to allow the Gentiles into his family just like Jews, that is through faith in the Messiah. The Jewish people had a real hard time with this because they only thought that someone could become right with God by coming Jewish.  

They were not given so many details of the New Covenant New Testament Church in the Old Testament. In particular the way the church was going to function was vastly different from the way the nation of Israel worked. It was a mystery to them. this is why Paul frequently uses the phrase mystery when he talks about the church and the relationship that God has with gentiles no differently from the relationship he has with Jews.

The new law would be written on people's hearts instead of relying upon the letter of the law. Gentiles would not need to convert to Judaism in order to be right with God. Many of the Jews wanted the Gentiles in the church to follow all the Jewish rules, including all males being circumcised. This created many conflicts in the early church.

Eph. 2:11-18

[11] Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
[12] That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
[13] But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
[14] For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us;
[15] Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;
[16] And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:
[17] And came and preached peace to you which were afar off, and to them that were nigh.
[18] For through him we both have access by one Spirit unto the Father.

Eph. 3:1-6

[1] For this cause I Paul, the prisoner of Jesus Christ for you Gentiles,
[2] If ye have heard of the dispensation of the grace of God which is given me to youward:
[3] How that by revelation he made known unto me the mystery; (as I wrote afore in few words,
[4] Whereby, when ye read, ye may understand my knowledge in the mystery of Christ)
[5] Which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit;
[6] That the Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel:

Eph. 4:4-6

[4] There is one body, and one Spirit, even as ye are called in one hope of your calling;
[5] One Lord, one faith, one baptism,
[6] One God and Father of all, who is above all, and through all, and in you all.

There was a strong reluctance and sometimes an outright refusal to let go of the old Covenant. The Jews had been told that God was going to make a new covenant with them. A covenant is an agreement between two parties. The Jews utterly failed in keeping their part of the Covenant that God had made with them. The arrival of their promised Messiah was bringing the New Covenant to them!

Though the Jewish leaders especially, and many lay people of the Jewish religion outright rejected Jesus Christ there were some that believed. As a result, every early church had at least some and sometimes a majority Jewish population.  

So much so that one of the letters that we have in the New Testament was written specifically to the Hebrews. it is called Hebrews.  

It is not clear who the author was because it was not signed as most of the letters were. There are some hints within the text that point in a certain direction but no names are given.

As time went on the church became largely Gentile, because the Jews continued to reject Jesus as their Messiah.

There were many conflicts in the early church due to some Jews insisting that the Gentiles essentially had to become Jewish still.  Much of the Apostle Paul's instruction was given to the churches in order to correct these errors.

Gal. 2:3-16

[3] But neither Titus, who was with me, being a Greek, was compelled to be circumcised:
[4] And that because of false brethren unawares brought in, who came in privily to spy out our liberty which we have in Christ Jesus, that they might bring us into bondage:
[5] To whom we gave place by subjection, no, not for an hour; that the truth of the gospel might continue with you.
[6] But of these who seemed to be somewhat, (whatsoever they were, it maketh no matter to me: God accepteth no man's person:) for they who seemed to be somewhat in conference added nothing to me:
[7] But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter;
[8] (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)
[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.
[10] Only they would that we should remember the poor; the same which I also was forward to do.
[11] But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed.
[12] For before that certain came from James, he did eat with the Gentiles: but when they were come, he withdrew and separated himself, fearing them which were of the circumcision.
[13] And the other Jews dissembled likewise with him; insomuch that Barnabas also was carried away with their dissimulation.
[14] But when I saw that they walked not uprightly according to the truth of the gospel, I said unto Peter before them all, If thou, being a Jew, livest after the manner of Gentiles, and not as do the Jews, why compellest thou the Gentiles to live as do the Jews?
[15] We who are Jews by nature, and not sinners of the Gentiles,
[16] Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.

 Gal. 5:1-6

[1] Stand fast therefore in the liberty wherewith Christ hath made us free, and be not entangled again with the yoke of bondage.
[2] Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing.
[3] For I testify again to every man that is circumcised, that he is a debtor to do the whole law.
[4] Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace.
[5] For we through the Spirit wait for the hope of righteousness by faith.
[6] For in Jesus Christ neither circumcision availeth anything, nor uncircumcision; but faith which worketh by love.