Getting back to the "cognitive bias" part, I think we have established that religious groups can:
a) Rejects another group because it doesn't understand that group, even though the other group has never committed an offence against them
b) Do not reject their own members, even though they commit the offences that they attribute to the out-group.
This is a cognitive bias - seeing the world in a way that does not reflect reality.
While this can certainly be true of religious groups it can also be true of any other grouping of humans that has existed or will exist. They have even shown a similar phenomena in completely random groups separated only by
t-shirt color.
What you have identified is referred to by psychologist as in-group favoritism.
https://en.m.wikipedia.org/wiki/In-group_favoritismThe two main theories regarding the cause of this are referred to as Realistic Conflict Theory and Social Identity Theory. In-group favoritism is essentially one of humanities built in flaws.
Religious organizations are made up of humans and thus not immune to humanities inherent flaws.