The most common and most likely answer to this crossword clue is the 8 letter word APOSTASY
I've seen this crossword clue in The Times
A
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More clues leading to the result APOSTASY
- A job so ungodly ultimately leading to giving up religion
- Renunciation of an appointment when meeting Yankee
- Backsliding secretary disheartened by job in support group
- A position, say, abandoned, in defection
- Leaving party or a job, say, after reorganisation
- Defection by saint who gets answer in a bunch of flowers
- A position, say, altered with the abandonment of one’s beliefs
- Indication of agreement to accept mail when services are abandoned because of this?
- Rejection of a job when variable
- Lack of faith in a job, say, after poor treatment
Buddy explains!

The straight part
We know that "giving up religion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case giving up religion = apostasy.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 APOSTASY mean?
APOSTASY noun- The renunciation of a belief or set of beliefs.
- Specifically, the renunciation of one's religion or faith.