Since you asked...

Surely we can commit as a nation to an advance in justice. My studies have taught me that the ethic of justice must be mutual respect (of a basic kind: taking one another into account).

The ethic of mutual respect already informs the theory of democracy. A nation with mutual respect as its ethic of justice would as a practical matter maximize the liberty that co-existing people can share. Mutual respect can be applied to the existing economy, with astonishing results for society: "For Crying Out Loud,, ACCEPT That A SOLUTION Actually EXISTS" (a "3 min read"--including options for further reading--here in Medium).

There is no belief upon which all citizens of this nation agree. That is why justice cannot be based on any belief. A requirement of mutual respect follows from observation within material existence: "Real Justice" (also here in Medium).

A requirement of mutual respect also follows from a belief in the moral equality of all people. The implications for society are the same. The existence of 'real justice' legitimates advocating for mutual respect as the ethic of justice based on a belief in equality: "Equality Is All We Need" (also here in Medium).