The idea of public reason has to do with how questions should be decided, but it doesn't tell you what are the good reasons or correct decisions.

A comprehensive doctrine, either religious or secular, aspires to cover all of life. I mean, if it's a religious doctrine, it talks about our relation to God and the universe; it has an ordering of all the virtues, not only political virtues but moral virtues as well, including the virtues of private life, and the rest. Now we may feel philosophically that it doesn't really cover everything, but it aims to cover everything, and a secular doctrine does also.

Different political views, even if they're all liberal, in the sense of supporting liberal constitutional democracy, undoubtedly have some notion of the common good in the form of the means provided to assure that people can make use of their liberties, and the like.

How did Madison get separation through Virginia and later Congress? The Baptists, the Presbyterians, and the smaller sects hated Jefferson; to them he was a secularist of the worst kind. But Madison could get Jefferson's bill passed because the Baptists, the Presbyterians, and smaller sects who were excluded in New England and in the South got together for their own protection.

If A were not allowed his better position, B would be even worse off than he is.

The principles of justice are chosen behind a veil of ignorance.

A political conception just applies to the basic structure of a society, its institutions, constitutional essentials, matters of basic justice and property, and so on.