Our observation from reading your study on The 7 Things You Have To Know To Understand End Times Prophecy is that for some time (second, minutes, hours?) after the rapture, the earth will be left with no church at all. I find this hard to believe. Also, the argument that God deals with the Church and Israel separately falls down in the case of saved Jews, as they are members of both.
Actually, the Earth will be left without the Church for at least 7 years, from the time of the rapture until the 2nd Coming, and even then we won’t return to Earth but will live in the New Jerusalem. Tribulation believers are not part of the Church, nor are believers who survive the Great Tribulation and go on to re-populate the Earth in the Millennium.
As for the existence of saved Jews denying the separation of Israel and the Church, you’re confusing individual Jewish people with the Nation of Israel. Paul said that in building the Church God took some from among the Gentiles and some from among the Jews and created a new race. (Ephes 2:15-16). In God’s view followers of Christ are no longer either Jew or Gentile but are called sons (children) of God (Galatians 3:26-28). As such, we are all part of the Church and will go in the rapture, leaving Israel and the Gentile nations behind.