What are some unique doctrines that a denomination holds that makes them distinct from others?

[The Liturgist]

Do they all differ by their doctrines? It looks like they declare one and the same Orthodox doctrine, but are not in communion with each other. Each one of their first hierarchs declares that he is the only legitimate successor of Metropolitan Vitaly.

Yes, schisms of this sort have occurred numerous times, and indeed happened with the Greeks as well due to the controversy caused by the Revised Julian Calendar. Now, my position is that the RJC has been a disaster - it is inherently, fundamentally flawed, since among its many problems is the fact that the number of days in the Apostle’s Fast can now be a negative number, causing it to end before it begins, which is absurd. However, the RJC does not justify the schismatic Old Calendarist jurisdictions.

Additionally, similiar eruptions of schismatic churches have occurred outside of Orthodoxy in response to various stimuli. There have also been cases where there is a lack of optimal unity among traditional churches left over after the mainline Protestant churches have themselves arguably gone into schism by embracing homosexual marriage and ignoring the plain words of Scripture and the tradition of the Christian Church that teaches that sodomy is a terrible sin. In these cases, I am not inclined to regard the remnant churches as schismatic, since they were abandoned by the mainline Protestants.

Obviously no Orthodox Church has embraced such false teaching, and I hope that none will, but many people including myself came over to Orthodoxy due to various problems with the mainline Protestant churches in which we grew up.