Is religious liberty about inclusion by the state or competition with the state?

Toronto law profs Ayelet Shachar and Ran Hirschi have posted their paper, "The New Wall of Separation: Permitting Diversity, Restricting Competition."  From the abstract:

In recent years, the specter of litigants turning to religious or customary sources of law as authoritative guides to regulate their behavior, alongside or in lieu of secular norms, has risen to the forefront of politics in many countries worldwide. In this essay, we draw upon citizenship theory and comparative constitutional jurisprudence to identify two different categories of judicial response to religious-based claims for recognition, accommodation, and exemption: 1) 'diversity as inclusion;' and 2) 'non-state law as competition.'

As long as legal claims for accommodation are not seen by courts as challenging the lexical superiority of the constitutional religion itself ('diversity as inclusion'), they stand a fair chance of success. Contrast that with the unyielding reluctance of legislatures and judiciaries to accept as binding or even cognizable any potentially competing legal order that originates in sacred or customary sources of identity and authority. This pattern of clamping down and refusing to accept any alternative sources of regulation becomes particularly visible where the legal challenge at issue is interpreted as raising doubts regarding which set of norms and institutions, or what set of high priests, should have the final word in authoritatively resolving legal disputes within a given society ('non-state law as competition'). This is a challenge that no secular legal order, no matter how tolerant and otherwise open to providing exemptions and accommodations to religious believers, can accept with indifference. For what perceived to be at stake here is the very authority and source of legitimacy of the accepted civil religion.

Is this "wall of separation" one that Catholic legal theory would support?  I have not read the paper, so I'm not entirely clear when the secular legal order's recognition of the binding nature of other normative claims on particular segments of the citizenry constitutes  "inclusion" or represents "competition."  The Church would support foundational rule of law concepts, but obviously insists on space in which citizens can live out their allegiance to claims that do not emanate from the state.  So is this framework helpful for navigating any of the tensions in American law, or just in societies grappling with more explicit questions of political pluralism, such as Canada and South Africa, both of which are discussed in the paper?  (It must be helpful for something, since it received Solum's seal of approval.)