The Invalidity of Atheism
I think maybe a more concrete example is how arithmetic informs calculus (you need arithmetic to do calculus but not vice versa). Whether you use a duodecimal system or decimal etc, and even how you do arithmetic (whether it's wrong or not) informs how the calculus problem will be (what digits are used and whether it's wrong or not or whether there are multiple answers).
In this same sense, culture simply doesn't have the ability to inform decisions like whether math/science are foundationalist and how they relate to each other (creation/causation narrative). An example of this is the Jesuits, and even ancient greeks up to archimedes and beyond, denying or banning infintesimals. This changed how math was done (more geometrically) and caused calculus to not be developed.
As for the last bit, I believe people pick what they believe is most true in any situation and existential crises happen when a really fundamental belief one holds is shown to not be as universally applicable so I believe trend towards a single foundation or fundamental truth but allow caveats either through ignorance or some more fundamental truth that guides when to choose between the two.