I have no idea whether David Barton is a reliable historian, but he certainly has his critics. For example, the liberal Baptist Joint Committee on Public Affairs has put forth a detailed
critique of Barton's "America's Godly Heritage". His source for the assertion that John Randolph of Roanoke was a Muslim also appears to be a biography of Randolph that is less reliable than Henry Adams' biography (although Barton seems to cite letters included in that autobiography instead of the tome itself - without looking at a copy, it would be impossible to know).
One of the things that distinguishes David Barton is the incredible number of original documents, books, letters, etc., he has in his library. He is very careful in his research and writing.