"Chosen people" means chosen by God because of descent from Abraham, Isaac, and Jacob:
Deuteronomy 10:14-15 KJV
Behold, the heaven and the heaven of heavens is the Lord's thy God, the earth also, with all that therein is. [15] Only the Lord had a delight in thy fathers to love them, and he chose their seed after them, even you above all people, as it is this day.
If a Chosenite rebels, and rejects Messiah, they are cut off and de-chosened:
Acts 3:22-23 KJV
For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you. [23] And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people.
Romans 2:25 KJV
For circumcision verily profiteth, if thou keep the law: but if thou be a breaker of the law, thy circumcision is made uncircumcision.
Romans 2:28-29 KJV
For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: [29] But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.
Meanwhile, the Israelis never were "chosen" because they are by and large NOT the descendants of Jacob.