It won't take much of a change in the climate before we see significant conflict over access to water. India and Pakistan have a treaty they both signed in 1960 regarding access to water from 6 rivers they share (https://en.wikipedia.org/wiki/Indus_Waters_Treaty). These are two nations that have nuclear weapons... if that treaty fails and results in a war, that'd almost certainly end up being World War III, and could very well result in the end of civilisation.
This isn't speculation on my part. We're already at the point where nations have civil wars over access to natural resources like water and agricultural land. It was a key factor in civil war in Sudan. Wars around the middle east between Israel and it's neighbours are rooted in religion but are often also about access to water from the Jordan basin.
Climate change isn't simply things getting hotter and sea levels rising. People literally go to war over resources. It really matters.