The New Covenant is made with the house of Israel [Ephraim], not with the house of Judah.
Both the OT and the NT say it is made with the house of Israel, and with the house of Judah.
Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Yes, I know he says that in Jer 31:31
But then he goes on to only specify the covenant with the house of Israel.
33But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
34And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
So how do you read this? Why does he leave out the house of Judah in these specific covenant blessings given to the house of Israel in Jer 33?
Is it because the house of Judah will receive them at a different time?
We see what is come upon the house of Judah [in general] in other passages--during this age--
In them is fulfilled the prophecy of Isaiah: "'You will be ever hearing but never understanding; you will be ever seeing but never perceiving. Mat 13:14
The question about whether or not inheriting the blessings of God is connected with one's order of birth, race, or ethnic background is addressed in the history of the Israelites and of Edom. Edom is a name for the descendants of Esau, Jacob's brother. Technically, Edom was the firstborn, but Jacob usurped him, obtaining the birthright and the blessing by stealth.
Before they were born, their mother learned that they represent two nations, and two manner of people
Genesis 25:21-2621 And Isaac intreated the LORD for his wife, because she was barren: and the LORD was intreated of him, and Rebekah his wife conceived.
22 And the children struggled together within her; and she said, If it be so, why am I thus? And she went to enquire of the LORD.
23 And the LORD said unto her, Two nations are in thy womb, and two manner of people shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger.
24 And when her days to be delivered were fulfilled, behold, there were twins in her womb.
25 And the first came out red, all over like an hairy garment; and they called his name Esau.
26 And after that came his brother out, and his hand took hold on Esau's heel; and his name was called Jacob: and Isaac was threescore years old when she bare them.
After Jacob received the blessing from Isaac, he was hated by Esau.
Genesis 27:41And Esau hated Jacob because of the blessing wherewith his father blessed him: and Esau said in his heart, The days of mourning for my father are at hand; then will I slay my brother Jacob.
Centuries later, when the Israelites were in the wilderness, Balaam gave a prophecy that said Edom would eventually be a possession of Israel.
Numbers 24:17-20there shall come a Star out of Jacob, and a Sceptre shall rise out of Israel, and shall smite the corners of Moab, and destroy all the children of Sheth.
And Edom shall be a possession, Seir also shall be a possession for his enemies; and Israel shall do valiantly.
Out of Jacob shall come he that shall have dominion, and shall destroy him that remaineth of the city.
And when he looked on Amalek, he took up his parable, and said, Amalek was the first of the nations; but his latter end shall be that he perish for ever.
In Isaiah, other prophecies speak of God's judgments falling upon Edom. Idumea was another name for Edom or Esau.
Isaiah 34:5-65 For my sword shall be bathed in heaven: behold, it shall come down upon Idumea, and upon the people of my curse, to judgment.
6 The sword of the LORD is filled with blood, it is made fat with fatness, and with the blood of lambs and goats, with the fat of the kidneys of rams: for the LORD hath a sacrifice in Bozrah, and a great slaughter in the land of Idumea.
Ezekiel also records similar prophecies.
Ezekiel 35:15As thou didst rejoice at the inheritance of the house of Israel, because it was desolate, so will I do unto thee: thou shalt be desolate, O mount Seir, and all Idumea, even all of it: and they shall know that I am the LORD.
Ezekiel 36:5Therefore thus saith the Lord GOD; Surely in the fire of my jealousy have I spoken against the residue of the heathen, and against all Idumea, which have appointed my land into their possession with the joy of all their heart, with despiteful minds, to cast it out for a prey.
The book of Obadiah is all about Edom. It predicts the complete destruction of the house of Esau.
Obadiah 1:18And the house of Jacob shall be a fire, and the house of Joseph a flame, and the house of Esau for stubble, and they shall kindle in them, and devour them; and there shall not be any remaining of the house of Esau; for the LORD hath spoken it.
In Malachi, Esau is said to be hated.
Malachi 1:3And I hated Esau, and laid his mountains and his heritage waste for the dragons of the wilderness.
This is quoted in the NT.
Romans 9:13As it is written, Jacob have I loved, but Esau have I hated.
It seems the whole concept of inheriting God's blessings because of birth is represented by Esau. Eventually they disappeared after becoming Jews. They were assimilated in the Jewish race. Today they are nowhere to be found.
OTOH, the covenant people become Israelites and inherit the promises, not by any ethnic connection, but by faith in Christ. This, I think, is the meaning behind the revelation given to Rebekah that her children represent two manner of people
One is a type of those who hope to inherit by right of birth, and the other, Jacob, represents those who obtain the blessing, by grace, and faith in Christ.