The most common and most likely answer to this crossword clue is the 14 letter word LATITUDINARIAN
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The straight part
We know that "broad-minded" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case broad-minded = latitudinarian.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 LATITUDINARIAN mean?
LATITUDINARIAN noun- A person who is tolerant of others' religious views.
- Not restrained; not confined by precise limits.
- Tolerant, especially of other people's religious views.
- Lax in moral or religious principles.