>>But I've not found any primary or objective secondary sources on how this went
It's definitely true. Progressivism is the memetic leftover of north-eastern US Mainline Protestantism. The poster above you makes the mistake of comparing it to actual religions, when progressivism has evolved to drop the religious components, which still makes its followers the cultural descendants of creepy religious maniacs even though they don't believe in a God (also, as a side note, consider that this makes progressives not "anti-American" as right wingers make them about to be, but "ultra-American" in the sense of trying to make the US progress into a more 'pure' and ethical state, as the Puritans wanted it to be. Edit: also consider that this might make the right/left 'culture war' more of a religious war between two protestant-influenced sects). This was mainly done for political power. Think about it, there is supposed to be a disconnect in the US between the state and religion, what better way for a memeplex to adapt to its environment then to drop the supernatural bits, and focus on propagating the values, mores, and aspirations of its believers through political power.
You asked for evidence, here is a number of excellent sources:
The main book you should read is "The Puritan Origins of AMerican Patriotism." That pretty much lays out the argument.
Also check out "The Making of An American Thinking Class: Intellectuals and Intelligentsia in Puritan Massachusetts." It makes the case that Puritans are the forefathers of American radicalism.
I also recommend these:
God's New Israel: Religious Interpretation of American Destiny.
The Protestant Ethic and the Spirit of Authoritarianism.
Hellfire Nation: The politics of sin in America.
Also check out Michael Burleigh's two books on political religions (Earthly Powers and Sacred Causes). This isn't an aberration of history. Religious movements often drop their supernatural components under the guise of 'reason' and 'rationality' so as to adapt to the culture and politics.
And if you are still not convinced, here is a large list by an American urban historian: http://www.amazon.com/A-History-of-American-Radicalism/lm/R2...
Edit: I also forgot to mention there is a blogger that writes about this topic often. I generally disagree with a lot of what he says, but he comes up with a number of primary and secondary sources for this historical hypothesis.
Here is one post that sums it up: http://unqualified-reservations.blogspot.com/2007/07/univers...
And the multi-part Open letter series is also good: http://unqualified-reservations.blogspot.com/2008/04/open-le...