This. The Final Solution and the extermination camps only happened in 1942, after every major player already entered the war. Eugenics was reasonably popular at the time, so that wasn't a reason to go to war either, and while the concentration camps were immoral and at the start of the war they were comparatively humane and not much out of line with what was deemed acceptable at the time (US internment of Japanese, Russian labor camps and the current ICE camps come to mind). The conditions drastically worsened as the camps filled up, but by that time Europe was already at war.
What Hitler did was terrible, but that's not the reason we had a war. "Germany (or Japan) might invade us next" is what was really in everyone's mind.