(Srry for the wall of text. The bottom paragraph is more important than the top two, which are just lore speculation)
I think the whole "Loyalist vs. Rebel Advent" thing (and even just plain Advent vs. Advent matches) can be described as two different clashing Unity networks.
They might be the same thing to an outsider, but to an Advent... there are srs differences that make the matter srs bsns.
But personally, I'd like to see culture be more than a colored line marching across a phase lane. It really needs to be better represented than that. Maybe if you zoom in close enough to a planet, you'll hear various transmissions and bits of dialogue that are unique to each faction and their loyalist/rebel sub-faction. It'd be mostly noise, but clear enough to make out a headline or blurb or political maxim if you listen close.
As for the open/closed societies discussion, I think each race is vulnerable to certain kinds of propaganda. And it really isn't directed at the political or military classes of society, but instead to the civilians who aren't really befitting from the war all that much.
For the TEC, the concept of the Unity is probably reinterpreted as a technological advance rather than a religion. Sure, the religious bits do come, but after they've gotten people hooked onto the idea of an "internet that's inside your head." And the Vasari's medical science is pretty appealing too. Plus, their propaganda probably tries to portray their war as a futile and ultimately dangerous endeavor - as they could claim that the time they spend defeating the TEC is time not spent preparing to flee the enemy. That's a legit argument.
For the Advent, there really is nothing more appealing like forgiveness. TEC propaganda is no doubt focused on trying to convince the Advent citizenry how much of a mistake it was to exile them way back when and if they just rejoined their fellow humans, then all would be made well and (after the Vasari are defeated) there'd be a state funded search for the Advent homeworld and every Advent who rejoins the TEC will get a house there. The TEC would probably even tell em they could keep their little Unity thing. As for the Vasari, same message as the TEC, only flavored more on collectivism and working together against a common foe. Big attempt to say that the Vasari migratory fleet is one big happy family, just like the Unity. It'd fly with some people, I'm sure.
For the Vasari, it'd be your classic liberation propaganda campaign. Go watch "The Longest Day" and skip to the part with the French Resistance listening to the radio. Exactly the same for the TEC and Advent, only with different rebel groups. Kinda like the CIA and KGB funding rival freedom fighters during the Cold War, only with the Nazis still around as a mutual foe. Half their day would be fighting the Vasari occupation forces and collaborators, the rest would be spent fighting rival freedom fighters. Yes, humanity is just that predictable.
All in all, each faction is pretty much just as hostile to outside ideas as any other (save the Vasari occupied populations, but you have to wonder what their culture actually looks like after a few generations of imperial rule), so anything that's in their propaganda has to be pretty careful not to step on any toes (so no "LOL EVERYTHING YOU BELIEVE IN IS WRONG") and really painting their side in a sympathetic light. The most common argument made by any propaganda writer is "We want to be friends, but because of X we're forced to fight this pointless war."
But enough theorizing on the lore.
What really needs to happen is a way for big empires to be politically stable. I mean, like with the TEC. They're technically reuniting various planets who were originally apart of the Trade Order anyway. As such, they really should be seen as the game goes on as the rightful heir to the Trade Order. Sure, when you go multiple TEC players, that's not going to happen, but if it's just you vs. a space nazi, I don't really see how a newly colonized planet would be at 15% allegiance. I mean, it's either you or mean looking aliens at that point. I don't really know what people on this planet are smoking.
And this is true from the perspective of every other faction. They all are capable of being big empires and justifying themselves politically to their populaces. Space is really really big. Everyone is pretty much so far away from each other that distances begin to become irrelevant as time goes on.
A separatist group on Mars would be just as mad at perceived imperialism from Earth as a separatist group in Alpha Centauri.
I'm not saying "get rid of the distance penalty." Oh no. Read the above sentence again. I'm all for it. In fact, I think it should be greater than what it is now at the start of the game, bringing it relevance to the smaller maps. There should be a long line of research, starting in the second tech level, that gives you greater and greater allegiance values farther and father from your capital.
Cause on a multi-system game, it's a big problem for everyone.
And you could play with various unique bonuses for each faction. Like, say, the Vasari might get an allegiance bonus if a Phase Stabilizer is present (cause it'd mean that the Vasari military can easily suppress rebellious activities) or perhaps all desert planets get allegiance bonuses for the Advent. You know, stuff like that.
Allegiance has really always been a mechanic that's completely out of the player's control. Sure, you can relocate your capital, but that just causes trades one low allegiance area for another. There really should be another solution for this.