We're already seeing an increase in natural disasters, with various areas experiencing floods, draughts or wildfires that didn't use to have them.
This alone leads to political conflicts in those areas, but also leads to mass emigrations, ultimately causing the political ~~egoists~~ right in unaffected areas being strengthened, which could at its worst lead to another Nazi uprising, world war etc..

I do also think that humanity as a whole will survive (that is, if we don't obliterate the ecosystems sustaining our lives, like e.g. pollinators). But our current life style of 8 billion people across all areas of Earth may not be sustainable anymore, which does mean the more privileged will be fine, others not.