The current fight will play out not in Saudi Arabia or Iran, but in Syria, Iraq, Lebanon and Yemen. Diplomatic breakthrough to these conflicts depends on the willingness of Saudi Arabia and Iran to pressure their proxies to make peace. The current enmity will make that nearly impossible for the foreseeable future.
It's an obvious analogy: There is a minority (mostly Sunni) elite ruling over a (mostly Shia) majority. The last few years have seen systematic discrimination, a repression of fundamental rights, and torture and deaths in custody. People aren't divided by race but by sect, which typically dictates where they live, what jobs they do, and whether they can achieve political power.