The reason I didn't put the others is because most of them are not really organizations who wish to topple a specific establishment. Ramza is trying to stop the Lucavi whio are manipulating the Church and the War but it's never stated that Ramza is actually trying to topple the Glabadoes Church.

Yuna's group does have the issues with the Maester's after Seymoure is killed but that's more personal and it never felt like the other Measter's cared (until they stormed Bevelle and learned the truth a little) but once again like Ramza's team, Yuna and company never change their objective to actually toppling the powers that be. Yes they get rid of the Maester's, but as anyone who saw that scene knows, it was completely unintentional.

As for the Al Bhed, once again the Al Bhed never actually try to stop Bevelle through military force, they tried to end the racial hatred of their clan by using Machina to destryo Sin thus proving the Maester's wrong and gaining acceptance. They never actually plan a military campaign or actually speak about overthrowing the powers that be.

Basically it come down to the fact these games featured established rebel organizations with some military power or at least the power to actually do something. These groups have specific goals and were not formed accidentally in the course of the game cause the group just happened to stumble upon the truth. In hindsight though, I should have mentioned the Death Corps. from Tactics though