Anyone having the time and interest should read this paper by Phillip Munoz on Religion & the Founding. I first saw him present this paper on CSPAN (this was truly a great show; it also had another scholar, from Grove City College, I do believe who discussed the "theistic rationalism" of the Framers). Now I've found Munoz's paper on the Internet.
Madison, accordingly, sought to separate ecclesiastical authority and political power. He sets forth his constitutional understanding of the principle for division in his famous “Memorial and Remonstrance,” an often cited but little understood document.
Article 1 of the “Memorial” states that because religious opinions cannot be coerced and because religious obligations are a duty precedent in time and authority to the claims of civil society, religion is an “unalienable” right. “Unalienable” has a precise and definite meaning for Madison. Unlike other natural rights such as property, which are transformed into civil rights upon entering the social compact (and thereby better secured), individuals cannot give up their natural right to religious freedom. Religion, Madison therefore concludes, is “exempt from the authority of the society at large” and “is wholly exempt from [civil society’s] cognizance.”
By “non-cognizance” Madison means that the state may not recognize or acknowledge the religious affiliation of individual citizens or associations of citizens. Literally, the state may not take religion into its view. To adapt a term from civil rights discourse, the state must remain “religion blind.” The state, therefore, may neither privilege nor penalize [Rowe's emphasis] a citizen or an organization on account of religious affiliation. It may not grant exclusive privileges to one sect or to all religions generally. Ecclesiastical establishments, accordingly, violate the legitimate constitutional authority of any social compact. By definition, they fail to respect the “unalienable” character of man’s natural right to religious liberty.
A majority of scholars and several Supreme Court justices have misinterpreted Madison as demanding a strict “wall of separation” between church and state. They fail to see the social compact framework of the “Memorial and Remonstrance,” and thus fail to see that Madison limits the state’s authority either to favor or disfavor religion. Just as the state may not single out Religious Liberty and the religion or religious citizens for beneficial preference, so the state may not exclude religious entities or religious individuals as such from generally available rights and privileges. To take one currently controverted point, according to Madison’s principle, if the state supports a general social service program, it may not exclude, on account of religion, religious individuals or religious associations from competing for government funds.
Now, Munoz is known for taking a conservative view on the Establishment Clause, but if he endorses this Madisonian interpretation of religion & government, this is a far cry from the conservative view that the Establishment Clause should be understood as a federalism only provision, one that only forbids the national government from erecting a national Church, and that government & religion should be able to intertwine themselves as much as they want after that.
Neutrality, "religion blindness," being able to neither "privilege nor penalize" religion are the standards that the Court should use to determine what degree of separation of Church & State is constitutionally required. Such a standard would explain why vouchers, for instance, do not violate the Constitution.
Conservatives might counter that Madison's & Jefferson's views weren't dominant at the time of the founding. But a natural rights approach to the Constitution would ask whether the Madisonian, Jeffersonian view is necessary to respect the doctrine of the Declaration of Independence. Therefore, someone like Justice Thomas, or the entire bunch at Claremont, for instance, should support the degree of separating Chuch & State that Jefferson and Madison called for in their respective Virginia documents.
[Update: Thanks to Positive Liberty for the discussion.]