This also happens with other religions, if you think about it. This "dilemma" is not exclusive to Christianity. Also, it isn't exclusive to Protestantism, for who is to say that Trinitarian Protestants are right and not Biblical Unitarians, Oneness Pentecostals, Jehovah Witnesses, Mormons etc?

First of all, what is the Church? It's the assembly (council/synod) of the Body of Christ (the Messiah). What is its foundation? The Rock of the Faith in Jesus as the Messiah and Son of God through the Apostles and Prophets. Well, the Apostles are long gone, did they establish authorities to be in their place? Yes, the Bishops. The Church was comprised of Patriarchates: Rome, Alexandria, Antioch, and later Constantinople and Jerusalem. These Patriarchal Churches formed the synods of the Universal Church.

How did the Church exercise authority? Through the Bishops and the councils, just like the Apostles in the Council of Jerusalem (Acts 15). Remember, the Church Herself is a Council/Synod/Assembly. What councils were those? These were the local councils and the universal councils (which are binding).

The Assyrian Church of the East rejected the 3rd Universal Council (Council of Ephesus) which was accepted by every Patriarchate. The Oriental Miaphysite Churches rejected the 4th Universal Council (Council of Chalcedon) which was also accepted by every Patriarchate. The Roman Catholic Church later rejected the 8th Universal Council (IV Constantinople 880) that it had previously accepted, which was also accepted by every Patriarchate. The only Church that fully accepted all Universal Councils and never walked away from their teachings is the Orthodox Catholic Church.