Richard Garnett, a professor of law and the Director of the Program on Church, State & Society at Notre Dame Law School, writes that
…the “separation of church and state,” correctly understood, denotes a structural arrangement involving institutions, a constitutional order in which the institutions of religion are distinct from, other than, and meaningfully independent of the institutions of government. So understood, “separation” is a principle of pluralism, of multiple and overlapping authorities, of competing loyalties and demands. It is a rule that limits the state and thereby clears out and protects a social space within which persons are formed and educated and without which the liberty of conscience is vulnerable.
He continues a little bit further in his essay by making what might seem to be a paradoxical point. A free and secular civil society requires the robust institutional freedom of religion.
… constitutionalism depends for its success on the existence and activities of non-state authorities. It should protect, but it also requires, self-governing religious communities that operate and evolve outside and independent of governments. It is a mistake to regard “religion” merely as a private practice, or even as a social phenomenon, to which constitutions respond or react. Instead, the ongoing enterprise of constitutionalism is one to which religious freedom contributes. Human rights depend for protection and flourishing not only on enforceable constraints on government but also on the structure of the social order. With respect to matters of polity, doctrine, leadership, and membership, the autonomy that religious institutions enjoy simultaneously contributes to and benefits from that structure.
Why is this? Because, “Just as freedom of speech depends on an infrastructure of free expression, freedom of religion depends on an infrastructure of religious freedom.” Some of this necessary infrastructure is generic in nature: “open and functioning courts, legal accommodations, and thriving communications networks.” Beyond these though there must also exist what he calls “a web of independent, thriving, and distinctive institutions that are self-governing in their appropriate spheres.” Unfortunately, as he observes, today “the infrastructure on which authentic freedom under law depends is neglected, under stress, and vulnerable.”
You can read the whole essay here.