I would suggest we can categorise three theological arguments that Christian Zionists makes in support of Israel. Now, it is acknowledged that not all proponents of Zionism will agree with all of this, and there is internal division, but I believe this list forms a broad basis for discussion.
1. The first is something we might all broadly agree with whether Zionist or not; that is that Christians should love Jews and support their peaceful existence and co-existence where ever they live, in the Holy Land or elsewhere. And because Jews have suffered through history they need a homeland, so why not the Holy Land? Furthermore, God has allowed Jews to live in the Holy Land and establish a state, at least in part of it by his permissive will, and we should not oppose that.
2. The second is a positive theological argument towards the divine right of Jews to live in the Holy Land. This position seeks to justify the expansion of land controlled by Jews because it is held that God has given it to them by Old Testament promises - from the Nile to the Euphrates. In extreme cases it assumes that Jews can do no wrong in defence of this right. This position is however debated sharply because it involves biblical interpretation concerning land and application of promises, and it is a position challenged by Christian supporters of Palestinians.
3. The third is a negative theology towards the Church that seeks to undermine the claim of Christendom to Old Testament Abrahamic promises. The traditional Pauline - Augustinian claim involves the doctrine that the Church is the legitimate continuity of Israel because it was formed by the Messiah-King Jesus and by Jewish disciples and fulfills Old Testament promises. The negative theological challenge to this is promoted by misrepresenting the Reformed Augustinian theology so that it is taught by Zionist proponents that the Reformed theology holds that God replaced Israel with the Church. It potentially sets up a false dichotomy through use of straw-man arguments by over emphasising replacement theology. Yes, supercessionism does exist in popular form, and it needs to be challenged, but the true nature of the Augustinian doctrine focuses instead upon the continuity of the City of God from Old to New Testaments; i.e. the Jerusalem that is free, eternal and above is being established on the Earth through the Christian mission as an extension of Israel’s mission. One may ask however whether the negative Zionist doctrine effectively undermines the strength of evangelical Christian faith because it encourages Christians to look upon the Church as a sort of social-club-for-Gentiles devoid of its inheritance in Jesus as the fulfilment of the promises to Abraham through Israel.
There are other questions that arise with these three positions as well.
Does position two effectively undermine position one because it increases tension in the Middle East by giving theological justification to take land belonging to others? Even many Jews in Palestine are worried about position two, and would exchange land for peace.
Does position three effectively provide support amongst Christians for position two?
Are positions two and three really necessary in order to support position one? Most Christians support position one without encouragement because of Christian duty. I would suggest that positions two and three are unnecessary and unhelpful in seeking to uphold position one.