Exactly who are these people in Israel today?

[an actual gun]

Virtually every Christian before the 1800s believed in supersessionism, not dispensationalism; even the old Protestant churches did not immediately reject every tenet of Church teaching. Dispensationalism really ratcheted up with the propagation of the Schofield reference Bible, and it became the more politically correct position for Christians to take after WW2 and this resurgent, what I would call Israelophilia of the modern era.



Most of the people we refer to as Jews in the western world are Ashkenazim who have a genetic admixture with Europeans. Jews worldwide be they Ashkenazim, Sephardim, Mizrahim, or any others, do not profess the faith of Abraham, Isaac and Jacob. They don't even keep the faith of the Sanhedrin at the time Jesus died. The Biblical Judaism died and modern rabbinical, Talmudic Judaism took its place. The second temple was destroyed. No third temple has been built. The Church is the new Israel and the people who believe in Christ are God's people regardless of their race, as despite our differences all men are equal in dignity before God. So we have a group of people who are only tangentially related, by several degrees of separation, from the religion of the Bible, even that which preceded the New Testament, but there are some who claim because of that geographical location, or some limited genealogy, some fragment of DNA, these people have some persistent, imperishable, special position that never changed? Jesus said not to be concerned with this very sort of thing.

Matthew Chapter 8

8 And the centurion making answer, said: Lord, I am not worthy that thou shouldst enter under my roof: but only say the word, and my servant shall be healed.
9 For I also am a man subject to authority, having under me soldiers; and I say to this, Go, and he goeth, and to another, Come, and he cometh, and to my servant, Do this, and he doeth it.
10 And Jesus hearing this, marvelled; and said to them that followed him: Amen I say to you, I have not found so great faith in Israel.
11 And I say to you that many shall come from the east and the west, and shall sit down with Abraham, and Isaac, and Jacob in the kingdom of heaven:
12 But the children of the kingdom shall be cast out into the exterior darkness: there shall be weeping and gnashing of teeth.
13 And Jesus said to the centurion: Go, and as thou hast believed, so be it done to thee. And the servant was healed at the same hour.

John Chapter 4

12 Art thou greater than our father Jacob, who gave us the well, and drank thereof himself, and his children, and his cattle?
13 Jesus answered, and said to her: Whosoever drinketh of this water, shall thirst again; but he that shall drink of the water that I will give him, shall not thirst for ever:
14 But the water that I will give him, shall become in him a fountain of water, springing up into life everlasting.
15 The woman saith to him: Sir, give me this water, that I may not thirst, nor come hither to draw.
...
20 Our fathers adored on this mountain, and you say, that at Jerusalem is the place where men must adore.
21 Jesus saith to her: Woman, believe me, that the hour cometh, when you shall neither on this mountain, nor in Jerusalem, adore the Father.
22 You adore that which you know not: we adore that which we know; for salvation is of the Jews.
23 But the hour cometh, and now is, when the true adorers shall adore the Father in spirit and in truth. For the Father also seeketh such to adore him.
24 God is a spirit; and they that adore him, must adore him in spirit and in truth.

St Paul specifically mentions genealogies as to be avoided for matters concerning the faith:

1st Timothy Chapter 1
4 Not to give heed to fables and endless genealogies: which furnish questions rather than the edification of God, which is in faith.

The passage in my signature also gives us teaching about the remnant. There is a new remnant just as Elias was referring to in his time, St. Paul makes the comparison to the Church, for those who were so concerned that Christ had called people to something that seems to be a departure but is a fulfillment, yet they cling to ways of idolatry and have bowed their knees to Baal. We can see when we read the Old Testament and New Testament an enormous amount of typology. St. Paul says he himself was born a Jew, so it's not like the Jews/Hebrews are a condemned people. Some of them were chosen by the grace of God to lead a new remnant. Others have had every opportunity to follow.

3 Lord, they have slain thy prophets, they have dug down thy altars; and I am left alone, and they seek my life.
4 But what saith the divine answer to him? I have left me seven thousand men, that have not bowed their knees to Baal.
5 Even so then at this present time also, there is a remnant saved according to the election of grace.