difference between "so the Pilgrims believed" and "and the Pilgrims believed so"

The meaning is the same. The difference is degree of support for the statement "God made his children prosperous." And that is not a strong difference.

Number 1. lists a belief of the Pilgrims. But because of the second part it kind-of sort-of lists it as only a belief of the Pilgrims, not as a statement of fact. It's nearly equivalent to "The Pilgrims believed that God made his children prosperous."

Number 2. states an idea as a fact. Then it also tells us the Pilgrims believed this fact. So No. 2 comes right out and claims a fact, where No. 1 only claims the Pilgrims believed a thing.

So it's really quite a minor difference in emphasis.