I figured this one out after submitting a help request to resolve an issue on an alt:
If a character has completed Exile’s Reach, but still has not completed the quests up to and including “What’s Your Specialty?” (or its Horde counterpart), then the quest A Celestial Invitation will be unable to activate on that character. It will say that the requirements aren’t met when clicking the quest item, despite the quest having no requirements.
This is surprisingly frustrating, as the quest becomes account wide once activated on any character, so the expectation is that any character could use activate it with the mailed quest item. There is no indication at all as to why the quest is failing, and it is never stated that the Exile’s Reach storyline will continue to block characters from questing after they leave the island. Since the item is soulbound instead of account- or warbound, there is no apparent recourse and no clear cause of the problem to the player; just a messed up achievement.
Please either find some way to indicate that quests blocked by the post-Exile’s Reach quests cannot be progressed because of it, or at least make the mailed item from A Celestial Achievement warbound.