There are various descriptors for people who strongly believe in whatever "their belief system" is
fundamentalist - maintains core beliefs
advocate - promotes a belief
gate keeper - maintains the standards of a belief
dyed-in-the-wool - can not change their belief
some of these may also have religious overtones, and have no explicit meaning in terms of "open mindedness", though usually if one has a very strong belief in something it may limit inclusion of other belief systems.
In your examples
is someone who believes in the "tradition" of "how things were or have been". Where as
means "genuine" without regard to the strength of belief.
Usually, additional context is necessary to bring together the disparate sides of "strong belief" and "inclusion"
He is a true believer in the free market system but still sympathetic to the social safety net
They advocate democracy while still respecting the monarch.
She is a dyed-in-the-wool Democrat while still wanting tax breaks.