Shinryu is unique among primals in that he was powered by vengeance, not faith. It's how he was able to exist independent of worshipers... somehow. I guess all Ala Mhigans' desire for vengeance worked, even if they didn't approve (or weren't aware) of Shinryu's existence? /shrug

Anyway... yes, Garlemald has a lot of faith in its ideals, which I find hilarious given its disdain for faith in favor of science. The issue they had wasn't lack of access to aether, but a genetic defect that rendered them incapable of manipulating it. As such they never developed magic, which is said to be a product of religion, and with no deities to worship or the ability to manipulate aether the Garleans would naturally be unable to summon primals. (Presumably everyone else in Ilsabard still can, though...)

With the development of Resonance, it's... possible that could change. Theoretically.