I want to talk about tempering

[Cilia]

What drives the Garlean war machine is, like Zenos says, mostly fear. They fear the consequences of religion, though it's important to note that their own actions often drive the greatest extreme (primal summons). One can argue that it's because they are aware that primals are one of the few things that can get in the way of their conquest, or that it's out of concern for the safety of the world... the truth likely lies somewhere in-between, but either way what they're doing is not helping matters. Regardless, fear is fear.

The Garleans have no known religion because they cannot use magic; somewhere (Encyclopedia Eorzea, I think - don't have one of my own) it was said that religion is a consequence of magic, so the magic-less Garleans being atheists makes in-universe sense. Lucia also suggests that the Garleans' atheism is a product of selfishness, as she genuinely adopted the Halonic faith after falling in love with Aymeric and going native in Ishgard. (Her exact line was something like, "You may think it strange for a daughter of Garlemald to be praying. But when I discovered something more precious to me than my own life, praying felt like a natural thing to do.")

[ObsidianFire]

Well, according to scholars, the first magics were derived from religious prayers in the 2nd Umbral Era. The 2nd Astral Era's governments were mainly Theocracies due to the power the religions could wield due to magic. In fact, it's not until the 3rd Umbral Era and Allag that magic and religion get decoupled from each other. And even Allag thought the Twelve was important in some way. It's just that magic was its own field of study by that point.

It's probably worth pointing out that we've yet to see a religion in FFXIV that doesn't make use of magic in some way. Religion and magic server to reinforce each other, either by religion leading to magic or magic giving people reason to believe that all that power has to come from somewhere. The concept of their being another realm other then the material realm almost certainly came more from religion then from magic. And the game even confirms that there is another realm that is comprised primarily of aether and that it's connected to the material realm in some way.

Of course, good luck verifying that when you and everyone else around you can't do anything with aether because you can never use it. As far as the Garleans are concerned, the only world that exists and matters is the one they're currently in. Aether is just another natural phenomina to study, not proof that there's another realm out there. As far as proving there's other realms out there goes, that would be tricky (dumping someone who considers themselves a scientist into the Void would probably do it though). They'd still need to figure out and know that messing with the atherial realm also has consequences for the material realm as well.

In fact, the only proof the Garleans have that religions are real is when primals get summoned. That's the only time we see higher powers out effecting the material realm in any major way. And it turns out that primals are really, really bad for the material realm. Meanwhile, the Garleans don't think that "something else is out there" and they've never summoned a primal (that we know of). The simplest explanation is that it's only the faith in something that doesn't exist in the material realm that causes a summoning. Given that the planet is in danger from that summoning, the Garleans might as well rid the world of the idea that worshiping higher powers is a valid option.

Of course, given what we've since learned from things like Bhamut's summoning, religion specifically has nothing to do with primal summoning. Faith/desire in something does, and the Garleans have a ton of faith and desire that their ideas are right. But that's a pretty complicated idea and one with no easy answers. And the Ascians probably don't want the Garleans to find out about that either.

[Enkidoh]

Except the Garleans have never regarded the Primals as anything other than false gods, not real ones. In fact, in 1.0 (although a fair bit of retconning has since taken place on this particular point), the Garlean term 'eikon' was actually a slur meant to degrade the very concept as simply some animal or beast that the ignorant and weak-minded worship as deities.

Of course, that has since changed slightly, but the Primals are still regarded as abominations by the Empire, and that it's blind faith by mortals that perpetrates it, thus in their eyes, pragmatic atheism is the only way to go (of course they come across as hypocrites though given they're constantly willing to use said false gods for their own ends, usually by consorting with the very forces that give rise to the means to create and summon Primals in the first place, but that's another barrel of moogles).