Is there a word for describing the existence of a unique or controversial interpretation of Christianity within a denomination? So obviously different sects or denominations have different interpretations and apply different emphasis to various teachings of the bible, but I'm wondering if there is a word to describe when a person or sect has a certain belief that is unique from other versions of Christianity. For instance, if someone believes that Jesus visited the Americas (Mormonism), or that he did not die in crucifixion and went on to have a family, or even something extremely trivial and specific like, for instance, (I'm just making this up off the top of my head) Jesus was a born as a breached birth. 

How could you say, "The Breachers  (again, I'm making this up and am not trying to be disrespectful) have a _________ where they believe Jesus was born as a breached birth." Is there a word that could fill that blank that would mean "a unique or controversial interpretation of a specific aspect of Christianity"?
A standard term for this is the noun distinctive.  It is used to identify the beliefs or practices that separate one denomination or tradition from another, as opposed to those beliefs that they have in common. 

For example, here are several examples of how this is used:


"Lutheran Theological Distinctives"
"Passing on the PCA distinctives to the next generation"
"Although the vast majority of Christian doctrines and beliefs are things that we hold in common, there are some 'Methodist distinctives,' and it is important for us to understand them." (source)
"[The] argument elevates aspects such as Anglican 'distinctives' in worship and liturgy, sacred time and space, decency or orderliness and sources of religious authority, at the expense of [...] more primary themes." (source)