Actually there's quite a bit that changes with the story.

NPCs will react to you differently depending on how far you are in the story or what city you started in or what GC you're affiliated with.

Crystal Brave's will show up throughout Eorzia after you've encountered them in the story.

The Scions move from Thanalan to Mor Dhona.

Of course the growth of Rev. Toll.

I'm actually quite surprised by the amount of things that actually change as you go through the story. Of course they can't do something like totally destroy a city but there are still big changes happening. But they are done in such a way that your progress doesn't affect another adventurers world.