Let us assume, for the moment, that Barton is correct. So what! The whole process of social and political evolution is to move history forward. There is no doubt that Christianity played a large part in the formation of this country, as it did in Europe - but that was then! Certain principles may still apply, but evolutionary forces will always modify them. History serves as a background to the studies of these forces of change - forces which will always be present, and will generally serve to improve rather than to worsen the societies affected. As a matter of fact, what radical Islam is attempting, I believe, is somewhat similar to what Barton is advocating - a return to historic principles with little concern for how societies have evolved!
The same holds true for the church-state issue. He may very well be correct in his interpretation of original intent. But so what! It's over. Events have progressed as our society has evolved into one far different from the one that was founded on these shores by English and Dutch settlers some 400 years ago! What was a principle at that time, has evolved into new principles acceptable to the society that adopted them.
In addition to expounding on the Jeffersonian or Washingtonian writings of the 18th century, one should consider what these giants would be ideating were they around in the 21st century!
History is a wonderful place to start. But it is only a start. Societies evolve, and their principles will necessarily evolve as well in order to adapt to society's changes. This is not to say that there are not certain principles, Judaeo-Christian or otherwise, that will always hold true, but we have to realize that the society of today can never again be the society of yesteryear. Though history can teach us much, it must constantly be considered in light of the present.
We should never become the prisoners of history. Our past can never be our future.