Personally, my take on the rebellion is as follows.
TEC - Rebels want to fight the aliens, loyalists want to ride out the fighting and persevere with minimal fighting
Vasari - Rebels don't think they are strong enough to fight the unknown enemy and want to ally with everyone to increase their odds of success, loyalists just want to keep running, they don't want to fight this unknown enemy if they can outrun it
Advent - Rebels don't believe their war with the Vasari is justified and that corruption within the Unity has led to their fighting two enemies when they really only have a quarrel with the TEC, loyalists simply want to destroy all who are in their way (kind of like TEC Rebels), especially the TEC
I'm not 100% sold on where these rebellions would originate (high up in the government, high in the military ranks or lower in the general population or amongst the lower ranking military personnel) but it can certainly be interpreted many ways.