1) Domination: fight it out and exterminate the other side or disenfranchise them so much they become powerless to oppose your agenda. Then you rule over them and make sure to keep them weak and defeated otherwise they will switch tables on you. (Examples: Bismarcks' original Kulturkampf reversing to Weimer reversing to Nazis, Argentina's dirty war)
2) Devolution: decentralize even more and reduce power of Federal government (Examples: Lebanon. Switzerland)
3) Divorce: split into two different nations entirely. (Examples: Ethiopia/Eritrea split, Yugoslavia breakup)
The reason why is that this is ultimately a religious war about values. People will die rather than give up their religion or change their core values. That means that if their core values are diametrically opposed, then will rather die than stop doing what the other side is convinced is immoral. This brings us to my favorite trilemma:
a) diversity (of values)
c) a strong central government
Personally, I favor devolution (best) or a national breakup (second best). Obviously I do not favor domination. But most people I know, and everyone I know on the left, favors domination. The right must be defeated.
But it's easy for me to emigrate to a nation which is much more sane than the U.S., so I have less at stake than those stuck in America.