John Smith, a member of my congregation, would be addressed as brother in face-to-face conversation. If I write a letter to him, should I capitalize this word? For example, as in:
Dear Brother Smith,
This supports @tchrist's analysis, but I thought I'd share the source material with you.
Here is a fairly straightforward explanation of the punctuation of the word "brother" used in religious communication from an online religion style book...
The "capitalize before a name but not otherwise" clause answers your question.
If you are using brother as a form of address, just as you might write Doctor Jones or President Obama or Deacon Williams, then yes, you would capitalize Brother John there. Compare all these:
Those are now all titles, and thus should be capitalized, particularly when used vocatively as you have here.