The most common and most likely answer to this crossword clue is the 6 letter word MORMON
I've seen this crossword clue in The Times
M
O
R
M
O
N
More clues leading to the result MORMON
Buddy explains!

The straight part
We know that "one of different faith" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one of different faith = mormon.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MORMON mean?
MORMON noun- Any of various dark-coloured Asian species of papilionid butterflies of the genus Papilio.