The most common and most likely answer to this crossword clue is the 7 letter word ISLAMIC
I've seen this crossword clue in The Guardian
I
S
L
A
M
I
C
More clues leading to the result ISLAMIC
- Terror group erroneously claim to be this
- Embracing pietism at last, is “secular” religious?
- Muslim claims I may be converted
- Religious claim is suspect
- In-charge carries mails about/pertaining to a particular religion
- Following a certain faith is false claim
- Type of calendar, found, counting backwards in hexadecimal/sixteens
- Religious doctor claims one should get injected
Buddy explains!

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