The most common and most likely answer to this crossword clue is the 11 letter word IDEOLOGICAL
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "based on beliefs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case based on beliefs = ideological.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 IDEOLOGICAL mean?
IDEOLOGICAL adjective- Of or pertaining to an ideology.
- Based on an ideology or misleading studies or statistics, especially based on the media or propaganda. Not based on scientific evidence or reality.