Richard Shenkman and others have written some charming and informative books on the untruths that are believed about American history. I won't link to any of them, because they are a varied lot, and every one of them has a current political agenda pretty obviously protruding from its snout. Some attempt to show that America wasn't really a Christian nation, or that business has always screwed people, or that founding fathers X,Y, and Z were actually thieves and child molesters. The others attempt to show that America was too Christian (Was nahhht! Was tooooo!), or that business as brought us all our good things and attitudes, or that our founders were even more noble than we imagined.
It all gets rather tiring, as summations of individuals and events seldom falls into neat categories. Bill Clinton and George Bush don't fall into neat categories, why should Adams and Madison?
Historians, both amateur and professional, leap to conclusions and tend to see what they want or expected. Some are rigorous or honest enough to see clearly, but it isn't any easier for them than for the rest of humanity. In the popular myth-buster books, I often have enough background to notice a misinterpreted claim, and I pass one along for you here.
Shenkman claims that the religiosity of the early Puritans was not really much greater than ours, and he sites as evidence for this that only about 50% of the population of colonial New England had church membership. That would seem a plausible conclusion, until you know the difference between church membership then and now. Many, in some towns most, people were not accepted for membership on first application to their churches. Some applied three and four times before being accepted, and some who applied were never received. Membership was regarded as an honor, because the Calvinists wanted the Church Visible not to include anyone who wasn't clearly in the Church Invisible. Interestingly, the honor was granted to women more often than men.
In that atmosphere, a lot of folks wouldn't go through the humiliation of applying unless they thought they had some chance of acceptance.
Be careful of the mythbusters on any side. Their stories are charming, but often miss important points.