Hah - you're reading some interesting stuff. Ethnic Israel, like all the nations of the earth, shall one day bow the knee to Jesus (Ps 72:8-11). So long as ethnic Israel does not believe in Jesus, however, she sits under God's condemnation and curse even as Gentile nations that don't believe in Jesus do. But the glorious promise is that all nations shall worship the Lord - including special promises that ethnic Israel shall (Rom 11:28-32).
But remember that the Church is the Israel of God in the NT - see Gal 6:16 and Phil 3:2-3 and 1 Pet 2:9ff and Eph 2:11-22. So are we "anti-Zionists"? Depends on what you mean: the Church is biblically Mt. Zion, the city of the Living God. So we are pro-Zionists in so far as we labor and strive to build up the Church.
If the question is, "Should we support ethnic Israel as a matter of biblical and theological necessity?" then I think that the answer is NO. That will make me an anti-Zionist in some minds because they define "Zion" as the physical city of Jerusalem. But Paul makes clear that the Church is the heavenly Jerusalem, the reality to which the earthly Jerusalem only pointed (Gal 4:21-31).
All of this is, in my mind, separate from the political question, "Should America favor Israel to the other Middle Eastern countries?" To that question I may or may not answer yes as a Christian - personally I answer Yes. But I do so because the nation Israel supports biblical values more faithfully than other Middle Eastern countries not because ethnic Israel is God's elect people. The Church is God's elect people (1 Pet 2:9-10).