I have a background in NLP (pre-LLM) and like to study extremist rhetoric, and, while I don't think you're being reductionist, it's a little more removed than that. I'd replace with "hate" with "problems and stress". Once you can attribute that stress to a group... that's when the hate develops. There are certain global powers who have recognized this and weaponized it. Agreeing with the most extreme of both sides, loudly, is the modern standard for propaganda.