Quests & Version 2.0

So I heard from some people that most of the game will dramatically change when 2.0 comes out. So far I love everything I have seen and eagerly await the new content. However, I have heard that the current quest storyline and all side quests will be wiped out and replaced when 2.0 comes out. Is this true? What about dungeons like "Shposhae" in La Noscea? Will they be wiped out and replaced?

I ask because I am the kind of weirdo gamer that gets really into the lore and storyline of a game and I like that MMO's like FFXI and FFXIV provide an entire world of it. However, should I be rushing to get my character up to snuff and complete the current content before 2.0 so I don't miss anything or can I relax a little?

The only stuff that is confirmed for removal is the Dalamud-related stuff (mainly Grand Company quests) as well as the Primal quests. I wouldn't expect dungeons to go anywhere.

Unless you want to risk burning yourself out, I'd just watch whatever cutscenes you think you'll miss on youtube or something.

Anything related to the seventh Umbral Era (Grand Company quests, Primal Battles, Sidequests concerning Dalamud, etc.) will be gone once 2.0 hits for obvious reasons. The dungeons will probably still be there, but they might look different. The entire world map is getting a redesign.

As for your specific example, I believe Yoshi-P said Shposhae would still be in 2.0, but it will be instanced.