Geology will inevitably affect civilization. if larger landmasses move slower and are often joined by smaller ones, coastal cities facing inward can be unreliable. Assuming the very edge is almost as uninhabitable as the fresh hot islands, of the ~10 000 years that any single piece of land exists it will only be habitable for about 5000-8000 (a very rough estimate) years.
Farmers have little cause to worry - one generation will not see all that much change. Villages might slowly move inward, at least trying to avoid going so far outward as to no longer have viable crops.
Big cities are more threatened - land still contorts every so often - presumably, two continents colliding creates earthquakes on both. Even on a comparatively stable world - our Earth, there are cities like Venice which are sinking fast.
A culture is unlikely to be too focused on specific geography - what is prime real estate now might be just a bit too cold a millenia from now. A unified language and religion would be more endemic to a faction.