The most common and most likely answer to this crossword clue is the 12 letter word SECTARIANISM
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "Narrowmindedness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case narrowmindedness = sectarianism.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 SECTARIANISM mean?
SECTARIANISM noun- Rigid adherence to a particular sect, denomination, ideology, or party.
- A political system in which power is shared among religious sects based on a constitutional formula distributing public offices among these sects