Just a guess here, but the Calvinist stress on literacy strongly connects it to the idealized version of a republican citizen. The school house is such an American thing, and it was very Protestant in origin. Through the New England churches local governmental decisions were argued over and voted on. Self government. Though other colonies had less democratic colonial governments, I know.
The historical narrative of a fight against the great centralized power of Rome, which inspired many to even greater flights of freedom from Calvinism itself which was a continuing drama in American Protestantism. So that legacy inspired.
Federalism is many ways reflects the way Protestant churches were themselves organized.
I think Calvinism strongly influenced the ideas behind republicanism. Let’s remember the first great awakening had already taken place, and it reflected so many issues in religion that were fought over for secular reasons later, freedom of thought and freedom to organize as many saw fit. So Calvinism was “relaxed” by 1788, but its influence in many ways weighed on the founders, imo