The Christian Arabs follow several different churches. The three main churches in Lebanon and Syria are the Greek Orthodox, the Maronites, and the Melkites. The Greek Orthodox Arabs follow exactly the same religion as the Orthodox Greeks, and for that matter the Russian Orthodox, etc. The Maronites and Melkites are more similar to the Catholic Church, but the Maronites are not in communion with Rome. In any case, these three follow essentially the same theology as European non-Protestant Christians. So their being Arabic-speaking has nothing to do with their theology.
The Chaldean Christians of Iraq have their own church, and I’m not familiar with where it belongs in relation to other Christian churches, but I don’t think their theology could be significantly different from the ones I already mentioned.
The Copts of Egypt follow a Monophysite theology for which they were persecuted under Byzantine rule. They share this with the (non-Arab) Ethiopian Coptic Church. We need a Polycarp or a tomndebb to explain exactly how these various Middle Eastern churches are different and how they are related.
The Palestinian Christians are Greek Orthodox; there are a few Anglicans among the Palestinians, including the Palestinian-American scholars Edward Said and Yvonne Haddad. There are also some Roman Catholic Arabs, I think, as well as Uniate Churches that are basically Catholic but follow non-Latin rites IIRC.
In any event, all these churches (except the Anglican) predate the linguistic change of their populations to speaking Arabic, and the Arabic language itself has no bearing on their theology. Their use of Allâh for God is simply a translation of the Greek ‘[symbol]o QeoV[/symbol] or the Latin Deus.