I think it's actually quite likely that quite a few "dominant" cultures - both in terms of nations and groups within nations - will effectively die out.

But humanity almost certainly won't? Why? Because there are sub-groups within humanity who have much higher fertility rates. As long as there are groups of people which are large enough to have viable genetic diversity, and recognise that a high birth rate is crucial for the continued existence of their culture, there will be humans.

Realistically, that means the decline of western liberal ideas and the growth of more extreme religious groups.