The Kirin Tor
The Kirin Tor is likely to take a very active interest in what's happening in Pandaria fairly soon. For starters, with the death of Rhonin at Theramore and the elevation of Jaina Proudmoore to the position of leadership means that any pretense of neutrality for this organization of magi is probably soon to be dispensed with, possibly sooner rather than later. Even if Garrosh Hellscream's mana bomb hadn't killed Rhonin, the decision of the Kirin Tor to interfere in the Horde invasion of Theramore revealed divided loyalties among its own membership, some choosing to support the Horde's invasion over the Kirin Tor's decision to try and prevent it.
The attempt to maintain Horde/Alliance neutrality in the face of Malygos' war on magic, the rise of Yogg-Saron in Ulduar and finally the push to confront Arthas may have all be wise, but they also opened up the mages to recruitment from both factions. In the absence of a Lich King or Deathwing to provide an enemy who demands a unified opposition, the Kirin Tor is no longer able to compel neutrality from its own membership, and its new leader is hardly one leading this by example. With Jaina at the helm, expect divisions and conflict as the Kirin Tor tries to decide how to react to the Alliance and Horde bringing their war to Pandaria.
The Argent Dawn, Order of the Ebon Blade, and Argent Crusade
These groups were all heavily involved and directed towards the undead hordes of the Scourge and the Lich King, specifically. Following Arthas' defeat, some of the Argent Crusade members have returned to the Plaguelands and taken up arms against the remaining Scourge as well as the Risen created by the dreadlord Balnazzar from fallen Scarlet Crusade members. Others have returned to the wandering lives of paladins and knight errants, crusading against evil in whatever forms they find it, no longer unified by the grand mission of defeating the seemingly-destroyed Lich King.
The Knights of the Ebon Blade, meanwhile, have fulfilled the organization's stated reason for existing - they've defeated their creator, avenged themselves for his betrayal of them at Light's Hope Chapel and his forcing them into a terrible demi-existence wracked by unholy magics that sustain them beyond their own deaths. With the Lich King's defeat, the Order as a group no longer has an overriding purpose pushing it onward, and as a result individual death knights are free to walk the earth as they see fit. Do you crave adventure and wish to travel to exotic lands? Then do so. Darion Mograine isn't going to tell you not to go to Pandaria, he's not your warden or your jailor.
The Cenarion Circle and the Earthen Ring
Both of these groups are most likely interested in the new land, revealed suddenly as the enshrouding mists part. It's a new place with extensive wild landscapes and entirely new kinds of elemental spirits, with several peoples that have shamanic traditions and nature magic unheard of elsewhere. However, both groups are also very occupied with trying to undo some or all of Deathwing's legacy of destruction - a mass exodus of Cenarion Circle druids or Earthen Ring shamans simply isn't in the cards right now.
This doesn't mean that no such members will travel to Pandaria, of course. Besides players, who are likely to represent the most adventurous of these organizations, there will doubtless be a few druids and shamans in the ranks of both the Alliance and the Horde, taking part in the invasion. But the Cenarion Circle and Earthen Ring as organizations are both unlikely to have the time or inclination to get involved directly in the Horde/Alliance conflict, at least not at first. There's simply too much to do back on Kalimdor and the Eastern Kingdoms, too much to repair and rebuild after the Aspect of Death's rampage.
Other organizations of interest
Some groups, like the Kor'kron and Seventh Legion, or SI:7, will of course be participating in the invasion, but these groups are linked to the Horde or Alliance and as such it's expected that they take part. Likewise, one wouldn't expect organizations primarily involved in Outland such as the Aldor or the Scyrers to arrive on Pandaria in force.
The lore of a group's involvement or lack thereof is fairly easy to ascertain. Essentially, do they have a reason to be involved, an opportunity to be involved, and a rationale for their involvement? Sure, the Earthen Ring's shamanic interests mean they might be interested in Pandaria, but it's hard to justify more than a token involvement for them as they have so much else going on and there's big Alliance and Horde armies making landfall, muddying up the works. Life on the rest of Azeroth doesn't stop just because there's max level adventurers running around somewhere new.
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