No, it's not, because the Church and its doctrines are historical and not to be made up on the spot to fulfill a political agenda. And just because it's also used that way by bad actors, doesn't mean it reflects the reality of the Christian tradition.

You're making a false equivalence simply because you believe Christianity to be an ideology and you oppose ideologies. So that's a category error too.

So the statement "Israel isn't the real church and the Catholics are not real Christians" is correct. The state of Israel is not the real Church and it never has been - this is a demented zionist interpretation that's not based on history or scripture. Catholics claim they have apostolic succession and are indeed the true Church of Christ who ordained Peter as its leader and who sent the Holy Spirit at Pentecost upon the apostles. So at least there's historicity and coherency behind their claim but still they officially fell away from the Church in 1054.