The Demi-Human War a protracted civil war fought in the Kingdom of Lugnica taking from approximately 50 BA (before arrival) to 40 BA, or fifty years before Natsuki Subaru's arrival in the new world, though calculating from Wilhelm's birth to the start of Ex 2, the war started in 48 BA, and ended nine years later, in 39 BA.
Initially a minor regional uprising on the Lugnican frontier, the war would slowly escalate into a bloody struggle of annihilation over the course of a decade. The two belligerents at the start of the war, the government of Lugnica, and the Demi-Human Alliance would themselves be relegated to minor players as the war spiraled out of control, turning into a nationwide ethnic conflict with skirmishes breaking out all over the country.
The eventual conflict was a result of over three-hundred and fifty years of tension between Humans and Demi-humans in the aftermath of the Great Calamity, where the Demi-Human races would wrongly become associated with the Witch of Envy. Numerous accounts describe how the war began, each of them differing. However the war may have started, it had unraveled all efforts of goodwill and definitively pit Demi-Humans and Humanity against eachother. Tens of thousands of combatants would be killed and countless civilians would be lost in senseless and often deliberate slaughter. Leadership on both sides would be whittled down and decentralized, and in the end the fighting ground down into a brutal war of attrition.
The war would end with the appearance of the Sword Saint, Theresia van Astrea at the Battle of the Trias Estate, roughly two years before the end of the war. Very shortly, the Demi-Human Alliance and rebellion collapsed, and the final encounter would be fought at the Second Battle of Castour Field. With that, an armistice was signed between the Kingdom and the Demi-Human Alliance.
The end of the war did not end prejudice between Humans and Demi-Humans, and in the following decades, much ill will would continue to be felt, especially in the countryside and especially concerning elves, though it cannot be said that relations have not improved. On relation to the story of Re:Zero, besides the obvious impact of being part of the world timeline, it is the origin story for Wilhelm van Astrea, Theresia van Astrea, and many others.
Though there is legitimacy to the idea that the war itself, taking place so long ago, does not necessarily affect the story, it is the event that has shaped the contemporary world of Re:Zero, whether the effects are visible or not.