Jeffrey Alexander treats religion as one of the uncivil spheres that surrounds the civil sphere. Religion makes a contribution to society, but it produces its own peculiar beliefs and hierarchies that ever threaten to intrude into the civil sphere. The civil sphere must do constant boundary maintenance and civil repair to keep religion in its place.
The civil sphere itself, in Alexander's account, has its own distinctive values and moral aspirations. It is, as he says several times, a project to create a democratic society. The overarching values of society reside there, which can be mobilized to trump and regulate the values of the uncivil spheres.
The values of a society get enacted and celebrated in rituals, something that Alexander, a good Durkheimian, would acknowledge. Celebrating the rituals of civil life helps create and renew solidarity in society as a whole.
In other words, the faith and practice of the civil sphere is the civil religion of society.
Civil religion is not part of the state, any more than voting, parties, or the norms of office are part of the state. Civil religion is one the ways in which the civil sphere regulates the other spheres, especially the state.
Civil religion has a complex relation with the universal religions that are (barely) contained in the religious sphere. They differ primarily in their Ultimate Concern -- God or Enlightenment in the case of universal religions, society itself in the case of civil religion.
Contrary to Alexander's hopeful, but maddeningly vague, picture of the contents of the civil values, it is not right to say that the ultimate concern of every civil sphere is democracy. As he notes repeatedly, each society's civil sphere is specific and historical. Its concerns are those of that society first, and perhaps of some higher global civil society only at the edges. And the object of veneration of civil religion, even the civil religion of a democratic society, is not democracy. It is the veneration of that particular society, its particular people, history, and manifest destiny.
The civil sphere does not put religion in its place. The civil sphere has a civil religion of its own.