The Barton perspective seems to romanticize early America, when regular church attendance was almost certainly much less than it is now, and where evangelical preachers were sometimes assailed by angry mobs. Secular history of the last century has dismissed early American religiosity almost entirely, ignoring the fact that cultural elites then, unlike now, were far likelier to be active churchmen who saw religion as essential to social cohesion.
Maybe there's been a slight turn-around in secular scholarship of early American religion. Ron Chernow's very good recent Washington: A Life declines to repeat the usual claim that Washington was an indifferent Deist. While admitting Washington's personal religious views were closely held, Chernow describes them as seriously felt and regularly practiced.
And maybe the Barton controversy will challenge other writers, secular and Christian, to address America's religious history with Barton's level of detail but with greater precision and context.