If the question is........"Are there still Jews existing today that claim they will always be God's chosen people?" Of course, obviously all Jews of all levels of Judaism from the Orthodox to the modern supposed progressive Jews of today claim that God would never abandon them as "THE CHOSEN".
What they ignore, clearly written in the Old Testament Text, is the fact that conditions were placed upon their being God's chosen people. "Now therefore, if you will obey My Voice (the voice of God) and keep My covenant, then you shall be a Special Treasure to ME (God), above all people; for all the earth is Mine." -- Ex. 19:5
What would happen if they failed to keep the covenant of Moses? God has never stated that Only Biblical Israel will remain God's chosen, there is no permanent "unconditional Election" reserved for the Jews only. The scriptures make it clear, what the Jews must expect if they continued breaking the righteous covenant of God, "Then I will sow her (election/chosen) in the earth, and I will have mercy on her who had not obtained mercy; then I will say to those who were not My people, 'You are My people!' And they shall say, "You are my God!" -- Hosea 2:23
The Apostle Paul, one of the most educated men in Jewish Law and Customs.....who studied under the feet of the highest ranking Jew of his day, "Gamaliel"....who was also responsible for the majority of the N.T. writings made it clear when he......in great detail referenced Hosea in relation to the Jews of his day......................
"As He (God) said also in Hosea: I (God) will call them My people, who were not My people and her beloved who was not beloved. And it shall come to pass in the place where it was said to them, 'You are not My people,' they shall be called the Sons of the Living God".....What shall we say then, That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith; But Israel, pursuing the Law of righteousness, has not attained to the law of righteousness. Why? Because they did not seek it by faith, but as it were, by the works of the law (of Moses). For they (the Jews) have stumbled at that stumbling stone". -- Romans 9:25-26, 30-32. Jesus was and is that stumbling stone as the corner stone in the Kingdom of the N.T. covenant. -- 2 Peter 2:4-8 Jesus and is the only "Son of Man"......born of a woman, born under the law, tempted like men in all ways........yet lived up to the literal letter of the Law of Moses from cradle to grave, Jesus was a practicing Orthodox Jew. (Gal. 4:4, 2 Corn. 5:21)
In the "eyes" of God........through Faith, not works under the old law..........there is neither Jew nor Gentile/Greek, slave nor free, male nor female........all are of one faith and the elect of God through Christ Jesus and heir to the promise made to father Abraham who was promised to be the father of many nations. --- Gal. 3:28-29
Contained in the Old Testament is the prophecy of God.........describing the N.T. church. The Jews who were guilty of breaking God's laws.......would have their status of God's chosen taken from them because they failed to live up to the letter of the Law.....so God would bring a new covenant that would apply to the entire world.......a Covenant written on the heart of the believers though faith, instead of laws written on stone. (Jer. 31:31-34) The new covenant would be "unlike" the Old Covenant of Moses.
Regardless........"It is a fearful thing to fall into the hands of the Living God." -- Heb. 10:32 One must swallow his/her pride and search the scriptures for truth, as that is the only way that God speaks to us today. There was a time past when God spoke through prophets and holy men.....but today He speaks only through His Son whom He has granted all authority in heaven and on earth (Matt. 28:18-19, Heb. 1:1) Today we have the "perfect law of liberty". (James 1:25) The N.T revelations of Christ Jesus which appoints all those of Faith as priests of a royal priesthood. -- 1 Peter 2:9
Each person is tasked with working out His/Her own salvation through faith and grace. There is only 1 sin that cannot be forgiven through prayer and righteousness.........the unrepentant sin. -- Phil. 2:12-13, 1 John 1:9