If either side is genuine about their beliefs, a first step is probably enforcing single-issue bills in Congress.
“Christianity” isn’t a unifying philosophy; even more recently than 50 years ago, the most dedicated evangelical/fundamentalist Protestant Christians were campaigning against the single largest Christian denomination in the country (Catholicism) as vigorously as against non-Christians, and many of our key religious freedom rulings were a result of Christian or Christian-adjacent groups (Jehovah’s Witnesses figure particularly prominently here) resisting impositions by more dominant Christian groups. Kennedy got much the same kind of attacks for being an (actual) Catholic as were directed at Obama for being (supposedly) a Muslim.
And if the short history in America were not enough, look at the troubled history of Christian-Christian relations in Europe and the Near East.
The problem I think is that you are starting from the assumption that America had a uniting mythos that only recently fell apart, rather than America having had deep, vicious internal divides throughout its entire history that were sometimes temporary subordinated to even stronger shared opposition to external forces.
> It wasn't always this vicious, or this pervasive in its viciousness, in my lifetime.
In our & our parents lifetimes, we had the "even stronger shared opposition to external forces" of Cold War opposition to the Soviet Union to keep these divisions in check.
America's divides have been terribly vicious in the past (https://en.wikipedia.org/wiki/Bleeding_Kansas, https://en.wikipedia.org/wiki/American_Civil_War), and some of the current things that divide us even have their roots in that era.
And even then, the Civil Rights and Anti-War and other internal conflicts of the 1950s-1970s weren't insignificant.