So I was watching Diarmaid Macolluch's History of Christianity BBC program, and he mentioned some older churches (such as the ethiopian). What sort of Doctrine did these churches stick to that led to them to split from the Christian Jews? Was there any communication between the members of these organizations with the European Churches?
I hope no one minds an Eastern Orthodox deacon commenting?
The Churches you mention are known as the Oriental Orthodox churches, and are not, in fact, older than the Byzantine and Latin churches. In fact, they split off from the Latin and Byzantine Church during the Council of Chalcedon over what today is considered simply a gross misunderstanding. As such, both the Roman Catholic and Eastern Orthodox churches are working very hard to restore communion with the Orientals.
As far as the theological split goes,it was about the nature of Christ.
The Chalcedonian orthodox position on Christ, that both Eastern Orthodox and Latin Catholics hold, is that Christ has a human nature and a divine nature. That is to say, he is fully man, and also fully God.
Think of it this way: He's not some specially anointed human, a super-prophet if you will, that just happens to be good at following God's will. He's also not just God walking among mortals, being shielded from the human experiences of temptation or suffering, overpowering evil with his mere presence. No, he's fully man - experiencing all the hardships and sorrows and doubts of human life and death. But also fully God, divine and just and merciful and all that.
The Orientals insisted that Christ has ONE nature. But, then, which one? Was he man? Or was he God? If we was man, then it makes no sense to worship him. It invalidates everything from the Nicene creed onwards. But, if he was God, then he knows nothing of what humanity is like. How could He, then, have suffered? What meaning does His passion have, and also his resurrection? It also invalidates everything, from the Nicene creed onwards.
It turns out, after so long, that the Orientals have (ahem) clarified their position. Christ is fully man and fully God. It's just that they didn't think these two aspects of him were ever in conflict. That is to say, he was never divided in opinion, the God side wanting to do one thing, and the Man side wanting to do another. So, it's not really one nature, it's just that the two natures of mankind and divinity are blended into one perfectly (miaphysite position).
The official position today is that the old problem was really just a mistranslation and misunderstanding. Who knows, that might be true - or it may be the greatest retcon in history. I don't know. But, it has allowed both sides of the conflict to make great strides towards unity, at least on the parish level. Many of our priests will now follow a don't ask, don't tell policy on receiving orientals into communion because of it, and so will theirs.
Your question is based on an incorrect premise and Diarmaid Macolluch's claim (as stated in your post) is incorrect. There oldest church is the One-Holy Apostolic Catholic Church, today with two branches (both claiming to be the original): the Roman Catholic Church and the Orthodox Catholic Church (aka the Eastern Orthodox Church).
There have been dozens of schisms and heresies in Christian history, such as Donatists and Arians, but these never became their own churches and all eventually faded or healed their schism. The only ones to do that have been the Protestants and the Oriental Orthodox, both of which are far younger than the original Catholic Churches.
Ethiopian Christians are most commonly Orthodox, and some would adhere to a splinter of the Orthodox Church called the Oriental Orthodox Church. /u/codesharp answered the Theological differences of the Oriental Orthodox plenty. As far as interaction, there was very little and this is part of why they remained split. The spread of the Caliphates strangled communication between Eastern Christianity and at some point the Orthodox churches were completely cut off from one another.