The most common and most likely answer to this crossword clue is the 4 letter word SUFI
I've seen this crossword clue in Financial Times
S
U
F
I
More clues leading to the result SUFI
- Commotion mostly over island’s religious mystic
- Muslim provided with American backing
- Supposing America brought back mysticism
- Backing provided for American holy man
- Primarily, spiritualist ultimately finding ihs?n?
- Mystic raising question about our identity
- Primarily, spiritualist ultimately finding ihsān?
- No end of bother over one mystic
Buddy explains!

The straight part
We know that "religious mystic" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case religious mystic = sufi.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.