HOUSEHOLD OF GOD are both Jews and Gentiles:

The Apostle Paul said: “Is he the God of the Jews only? is he not also of the Gentiles? Yes, of the Gentiles also:” (Romans 3:29).

“For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office” (Romans 11:13).

Therefore, any church denomination claiming to be the remnant of Israel, the natural branches of all the tribes of Israel - God’s chosen people (Jeremiah 31:1) must be reminded that God sent his only begotten Son, Jesus to this earth for “a light to lighten the Gentiles, and the glory of thy people Israel” (Luke 2:32).

Let us never forget what Jesus communicated with the Samaritan woman by the well, saying: “Ye worship ye know not what: we know what we worship: for salvation is of the Jews” (John 4:22-24).

Furthermore, the Apostle Paul said: “I say then, hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.  God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? How he maketh intercession to God against Israel, saying, ‘Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.’ But what saith the answer of God unto him? ‘I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.’ Even so then at this present time also there is a remnant according to the election of grace” (Romans 11:1-5).

“Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee. Thou wilt say then, ‘The branches were broken off, that I might be graffed in.’ Well, because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear: for if God spared not the natural branches, take heed lest he also spare not thee” (Romans 11:18-21).

Paul elaborated said: “The Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel” (Ephesians 3:6)

Paul explained that the Gentiles should be  co-inheritors with the Jews, said:

“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. But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ. For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us; [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; and that he might reconcile both unto God in one body by the cross, having slain the enmity thereby: and came and preached peace to you which were afar off, and to them that were nigh. For through him we both have access by one Spirit unto the Father. Now therefore ye are no more strangers and foreigners, but fellow citizens with the saints, and of the [HOUSEHOLD OF GOD]” (Ephesians 2:12–19).