The most common and most likely answer to this crossword clue is the 6 letter word UNLIKE
I've seen this crossword clue in The Guardian
U
N
L
I
K
E
Buddy explains!

The straight part
We know that "Out of character/to withdraw Facebook approval" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case out of character/to withdraw facebook approval = unlike.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 UNLIKE mean?
UNLIKE noun- Something that is not like something else; something different.
- Not like; dissimilar (to); having no resemblance.
- Unequal.
- Not likely; improbable; unlikely.
- Differently from; not in a like or similar manner.
- In contrast with; as opposed to.
- Not typical of one's character or personality.
- The act of withdrawing one's like from a post on social media.
- To dislike.
- To withdraw support for a particular thing, especially on social networking websites.