As both types of Earth's invaded by their respective enigmatic, parasitical spore-based hive-minds. This Earth got invaded by the Slag while the SI's Earth invaded by the Tyrum Consciousness though this International Coalition (precursor of the GTU) able to fight against that hivemind for 7 years during their First Contact War then reorganized into the Federal Dominant-party Stratocracy gov for the GTU. Which there ain't Keo nor similar religious stuffs.
BTW the GTU's flag was an improvised symbol initially meant to mark the location of hidden munitions and clandestine airdrops slowly grew into a worldwide symbol of defiance against the Tyrum during the First Contact War.
Check out these links for more details about what I'm talking about.
In 2200, mankind (as in the GTU) has journeyed to the stars to seek vengeance on their old enemy (Tyrum) and extend their power across the galaxy.
Greater Terran Union | Stellaris Invicta Season 1
https://stellarisinvicta.fandom.com/wiki/Greater_Terran_Union
https://stellarisinvicta.fandom.com/wiki/Tyrum_Consciousness
https://tvtropes.org/pmwiki/pmwiki.php/LetsPlay/StellarisInvicta
https://shop.templin.institute/collections/the-greater-terran-union-collection