Kira Talith
Kinetic Communication at its finest my Chick-e-dee
What is the Jedi Academy?
The intent of the Jedi Academy network is to make a network of Jedi Academies. Some of them are more or less affiliated with the Republic, but the academy network doesn't take a political stance any more than it would have the means or will to compel or guilt an academy or a specific teacher into taking students who don't fit their specific brand of jedi-ness.
It's an acknowledgement that the jedi order is too large and too diverse to be under one roof, as well as a statement that the costly, bitter schisms we've already seen are bad for what it means to be Jedi, not to mention bad for the survival of the Order's teachings.
It's an acknowledgement that existing structures and allegiances are more or less important to different Jedi, but that regardless of pique, opinions, or prevailing political and strategic winds, there should always be a cooperative connection between Jedi academies, and that the jedi principles need to be protected as well as freely discussed in an independent and non-political forum.
It's a statement that the most important thing is not making judgments about other Jedi's allegiances and interpretations of the Code. The most important thing is working together to create new Jedi who can make moral judgments on their own and giving new Jedi options of different environments that prioritize different skills, Code interpretations, and degrees of allegiance, but all within the bounds of Jedi tradition.
Jedi tradition includes a wide variety of those things, a healthy internal debate and tolerance. The academies and their Housemasters coordinate over major incidents, but the academy network isn't a power structure and has zero patience for those who try to set up power structures with themselves at the head.
If people set themselves up in power positions, the Academy network takes no stance on that, encouraging all its members to decide for themselves whether they recognize, say, a head of all Jedi functions X or Y. The academy network might facilitate convocations where many jedi could discuss roles and issues, but the academy network generally doesn't appoint people to any position that doesn't involve some training function in specific academies.
In summary, The Jedi Academy is not a central coordination function for Jedi. It's a coordination mechanism for existing Jedi training centers.