Today, are Jewish believers part of Israel or part of the Church?
At the cross the Lord did nothing less than create a new race of human. Ephesians 2:14-17 says some of this new race were formerly Jews and some were formerly Gentiles. Now they’re neither but are called the Church. Paul went to great pains to make this distinction. For example in 1 Cor. 10:32 he said we should be careful not to cause anyone to stumble, whether Jews, Greeks (gentiles) or the Church of God. And in Galatians 3:28 he said among those who are in Christ there is neither Jew nor Gentile, but all are one in Him.
For historical reasons that are understandable, some Jewish believers are reluctant to consider themselves part of the Church. But the Bible is clear in identifying them as such, and they will share the Church’s destiny, which is to be taken in the Rapture to dwell in the New Jerusalem as co-heirs with Christ in His inheritance.