David Barton is not a credible source. He's an amateur hobbyist who dabbles in pseudo-history and whose books have been repeatedly debunked owing to inaccuracies, omissions, and outright fabrications. His book "The Jefferson Lies" was dropped by its Christian publishing house for these reasons.

Here's a take down of his work by a pair of Christian conservative historians who, contrary to Baron, believe truth matters:

https://world.wng.org/2013/01/david_barton_is_wrong

The Baptist Joint Committee for Religious Liberty has no use for him either:

http://bjconline.org/a-critique-of-david-bartons-views-on-church-and-state/