Synonyms of the word 
UNDOGMATIC → BROAD-MINDED - LATITUDINARIAN
undogmatic
- adj. Not dogmatic.
broad-minded
- adj. Having an open mind; tolerant of diversity.
latitudinarian
- adj. Not restrained; not confined by precise limits.
- adj. Tolerant, especially of other people's religious views.
- adj. Lax in moral or religious principles.
- n. A person who is tolerant of others' religious views.
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