Wars are always fought over resources and/or ego. The wizarding world will go to war if one group has something another group wants, or if one group feels aggrieved and can only be appeased by punishing/subjugating the other group.
It was easy to see what caused this: an extremely power Dark wizard, a corupt government, a corupt press, old prejudices, and a dozen other factors. Putting magic into prospective, what could some of these factors be?
While magic can't create food or water, it certainly makes it a lot easier to acquire it, especially in places where the Muggles don't have the means to resist you. So I don't think wizards, even in Sudan, are likely to starve. There are too many ways for them to take what they need, or else just leave, an option not available to the unfortunate Muggles. So even a global environmental catastrophe would probably affect wizards less than others. Unless the human race itself is facing extinction, wizards will be able to survive.
I also wonder what it would actually take to make the two worlds intertwine. Because of Gamp's Law of Transfiguration, we know that food and other scarcities can be a factor this. Would other environmental disasters would it take to throw the wizarding world into chaos? What is magic capable of keeping people safe and what can't it keep people safe from?