What is the classification for a brother/sister in a fraternal religious order? [closed]

You may want to use the term fellowship instead. Although all dictionaries might not include this meaning, it is used in some religious environments:

a friendly feeling that exists between people who have a shared interest or are doing something as a group:

• He enjoyed the fellowship of other actors in the company. Christian fellowship (Cambridge)

Collins mentions it too:

A Church or religious association. The state or relationship of being a fellow.

Also, the word brotherhood can serve in this purpose:

A feeling of shared interests and support among men, or more generally, among all humans.
A brotherhood is also the membership of an organization of men, or the organization itself. (Cambridge)

The corresponding term sisterhood also exists specifically for women:

a society of women living a religious life (Cambridge)