That's a good question, and one that would probably require a book to answer.

What I can say is that religion was a multifaceted force that permeated politics and economics, and certainly influenced them, but perhaps not as much as you might think.

One of the easy mistakes to make, especially when we first start studying colonial America, is to assume that all British colonies shared a singular, monolithic culture. This was far from the case. British America's regions were divided starkly by ethnic makeup, economic cornerstones, and, yes, religion. New England was largely Calvinist and exclusive of dissenting faiths, though Rhode Island was known to be religiously tolerant. Pennsylvania likewise tolerated religious differences. Maryland was ostensibly Catholic, and ruled by Catholics, but the majority were Protestant. Among the elites of many British colonies, especially the central and southern, deism was popular. Though not a majority in any colony or city, Jews were also present and sometimes quite prominent members of their communities.

Here we come to the heart of your question: how did it help America grow, or did it? The plurality of faiths was partially reconciled with the Great Awakening. The mid-eighteenth century witnessed a massive revival movement, with itinerant preachers wandering up and down the colonies and preaching a message of shared Christianity and individual connections to Christ. It helped to blur the lines between many of the religious affiliations in the colonies. Though it had little effect on Catholics, Anglicans, and Baptists, the Great Awakening undeniably touched many, many others.

This is important to your question because it contributed toward a shared culture. The shared experience of the Great Awakening connected most of the the disparate colonies on a spiritual level. There were many other factors in this shared culture, such as the growth of print media, colonial success in warfare, increasing national pride, and the general impact of the acts of Parliament following the French and Indian War, to name a few.

To be somewhat teleological, religion helped the colonies grow together into a shared culture that would enable their cooperation in the American Revolution.