The Advent loyalists seek to prosecute their vengeance on the TEC and assimilate any rival population into the Unity.
That's hardly cooperation with other factions, as their titan says: "They will join us or die!" - not very diplomatic language.
I see the loyalist policy as one of unyielding conquest with few compromises with other races.
While their fleet is subjugating one part of the galaxy, other factions would take the opportunity to attack their empire somewhere else, hence the suggestion for new defensive techs.
The description for the rebels is a little ambiguous "Suspecting that a corruptive influence within the Unity has influenced their race, the Advent Rebels seek to purge this unseen enemy to restore the Unity to its proper path."
It could be interpreted as self examination to put the Unity back on an enlightened track or as a call to lash out in the hope of defeating the "unseen enemy".
I took the former interpretation where the "unseen enemy" could be something like a loyalist 5th column within the rebel faction which would need to be purged.
Unlike the loyalists, revenge upon the TEC is no longer seems a high priority for the rebels, which would allow them to eventually respect and work with other races.
Hence why I suggested some goodies for their diplomacy tree.