Jesus' true followers are Spiritual Israelite.
You are absolutely correct. The physical nation of Israel was replaced by the Christian congregation because Israel failed to accept the Messiah---Jesus of Nazareth. How could they continue to be His special people when they refused to accept Jesus (the Son of God; the Messiah)? Jesus himself spoke about this reality:
"The kingdom of God will be taken away from you [the chief priests and elders] and given to a people producing the fruit of it." (Matthew 21:43, NASB)
"Jerusalem, Jerusalem, who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, the way a hen gathers her chicks under her wings,
and you were unwilling. Behold,
your house is being left to you desolate!" (Matthew 23:37,38, NASB)
Then his disciples reiterated what Jesus had said.
"Simeon has related how God first concerned Himself about
taking from among the Gentiles a people for His name." (Acts 15:14, NASB)
"There is neither Jew nor Greek...for you are ALL one person in union with Christ Jesus. Moreover,
if you belong to Christ, you are really Abraham's seed, heirs with reference to a promise." (Galatians 3:28,29)
"Neither is circumcision anything nor is uncircumcision, but a new creation is something. All those who will walk orderly by this rule of conduct, upon them be peace and mercy, even upon
the Israel of God." (Galatians 6:15,16) You will notice that Paul was referring to those who accepted the 'cross' of Christ (verses 12-14).
"YOU [the Christian congregation] are a 'chosen race, a royal priesthood,
a holy nation, a people for special possession, that you should declare abroad the excellencies' of the one that called you out of darkness into his wonderful light. For you were once not a people, but
are now God's people." (I Peter 2:9,10)
Some people object to "replacement theology," but it is scripturally true and sound.