Actually the word Magi is where we get the english word for magic. The root of the word is from Persian. In the ancient Armenian they are called mohks, which, by today's standards means magicians. Mithras was believed to be the son of god and the savior of the world. Zoroastrianism the has the ideas of monotheism, since they were the first monotheists, they believed in some kind of a holy spirit, a virgin birth, baptism and some other philosophies in which would make them gravitate toward Christianity.
There is also Christ expressing himself as the Truth, the Way, the Light, the Door, which are all apart of eastern religions but Christs sets himself as the ultimate definition for what people are seeking in eastern religions as well as western religions of that time. To limit Christians to being Jews, Greeks, Romans etc. is quite trivial due to the fact that what Christ is, appeals to everyone.
Now that being said, there was not an elite group of catholic, orthodox, apostolic etc. that could claim that they were the sole proprietor of the Church. Thats why it was necessary to establish apostolic lineage and councils. The biggest problem of that time was the Gnostics. In the NT the Apostles re-iterate to us to stick to what they have been teaching specifically. The reason being there were a lot of people who listened to Christs sermons and teachings, and these people gather different opinions about what Christ taught. Remember when Christ taught there were hundreds if not thousands of people listening.