It's more or less an accurate statement insofar as the entire Bill of Rights was designed to apply to the Federal, not the state governments. I think the larger point that needs to be appreciated -- it's not just that "religion" was left to the states -- but that the original US Constitution was, by today's standard, a document that left the Federal government with an extremely limited reach. In many ways the US Founding from 1776-1791 was something "revolutionary," "anti-traditional," "enlightened" and simply "not Christian" (at least not in the traditional sense, certainly not in the reformed Calvinist sense).
Yet, the anti-traditional revolutionary implications of the American Founding are tethered greatly by the limited reach of the US Constitution as originally understood. It was a secular Godless document, but one whose secular godlessness was powerless to enforce against state and local governments.
In that sense, the American Founding was a very limited event. It was limited by the anti-statist, limited enumerated powers vision of the framers of the original Constitution. In other words, whatever was subversive about the ideals of the American Founders, they originally limited their own ability to "subvert" much of anything (including slavery) by establishing a very weak federal government.