There was a change under the new covenant, under the gospel of Christ in the definition of the house of Israel.
Under the old covenant, the house of Israel were all who were born of the ancestry of Jacob, and his twelve sons, the twelve tribes of Israel. (Gen 49:28) This was the promise given to Jacob / Israel's grandfather, Abraham.
When sending Jacob to his uncle's house to find a wife, Isaac told Jacob in Gen. 28:3-4,
"3 and God Almighty doth bless thee, and make thee fruitful, and multiply thee, and thou hast become an assembly of peoples; 4 and He doth give to thee the blessing of Abraham, to thee and to thy seed with thee, to cause thee to possess the land of thy sojournings, which God gave to Abraham.'" (KJV) Bold emphasis mine.
Under the new covenant, all who are baptized into Christ are counted for the seed of Abraham. Rom. 9:7-8,
"7 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. 8 That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed." (KJV)
Gal. 3:6-7, 27-29 establishes that adoption:
"6 Even as Abraham believed God, and it was accounted to him for righteousness. 7 Know ye therefore that they which are of faith, the same are the children of Abraham. 8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed." (KJV)
"27 For as many of you as have been baptized into Christ have put on Christ.
28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. 29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise." (KJV)
Under the new covenant, birth lines no longer matter, as there is neither Jew nor Greek, male nor female.. but only those in Christ, or those not in Christ. Under the new covenant those that are in Christ are of the seed of Abraham, counted for the birth line seed, and are now Israel.
Under the new covenant the house of Israel are all those in Christ.
So, those that are given the right to become children of God are those that hear the word (Rom. 10:10-17), and believe that Christ is the Son of God. (John 11:11-13) Those who had rejected Him were the very ones He was sent to call (Matt. 15:24, the Judeans, the lost sheep of the house of Israel), and they no longer had that right because they did not believe.
Having the right does not automatically complete or seal the deal. They can hear and they can choose to believe, but they have to answer the call.
Peter told those on the day of Pentecost what they should do. Acts 2:37-38;
"Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do? 38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins,..."
Ananias told Saul / Paul what he had to do. Acts 22:16,
" And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord."
There is only one way and that is through Jesus Christ, as only He is the way, the truth and life. No one comes to the Father but by Him. (John 14:6)
Therefore, if anyone hears the word, and believes that Christ is the Son of God, they have faith in Him, and the right to become of the seed of Abraham through Christ Jesus. But, they have to take the action, they have to answer the call to be put into Christ's body and be counted for the seed of adoption.
1 Cor. 12:13 -
"For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit."
There are not two ways. There is now only one way, and that is through Jesus Christ. We have to be baptized into Christ to receive the promise of inheritance. (Mark 16:16; Acts 20:32; 26:18; Rom. 6:3; Col. 3:24; Heb 9:15)
If you are interested, there are two posts at my blog which provide more scriptural evidences on God's Definitions Part I -The House of Israel, & Part II - The House of God, and how these definitions changed under the new covenant of the gospel of Christ. SeeShreddingTheVeil