Just want to say I love every inch of your analysis here, thanks for writing in! There are elements I'm unsure about and would love to discuss, gonna mention those below.
First, I do find your way of framing atheism versus agnosticism re:Garleans interesting and different from how I generally conceptualize those points. To my personal understanding, I'd classify atheism as more not believing in a higher power (how I'd classify Garleans) whereas agnosticism is doubt/uncertainty in a higher power. By connection with this, it has been established that Garleans absolutely believe in primals and that Eorzean faith has the power to create primals. However, primals are notably not the same as gods. Even in instances of beast tribes it is firmly established that primals are taken as perversions of god concepts by devotees rather than true gods themselves. This can be shown in the Vira Ananta's view of primal Lashmi, which they see as a simplified perversion of their goddess through the limited lens of mortality. For this reason, the Vira not only have zero problem with the Warrior of Light slaying the Qalyana primal--they actively endorse it. Primal Lakshmi, to them, is not only a false depiction of their goddess, she's outright blasphemous and a dangerous insult to the real Lakshmi.
If we take this concept further, primals can be taken as a form of idolatry in the sense that they twist something divine and inherently beyond mortal comprehension then attempt to force worship of a divine concept through symbols into something limited, literal, and inherently corrupted by mortal shortcomings instead. It replaces worship of the divine concept with worship of the symbol for that concept, if that makes sense. It's the difference between worshipping Lakshmi as freedom itself and worshipping Lakshmi as the most beautiful, happy snake woman ever.
(Disclaimer, I'm discussing this as someone who has studied religion outside of my gaming activity haha. In before someone says "not that deep", don't underestimate human ingenuity with this stuff! SE devs are super well read and have scattered a ton of thoughtful, intercultural religious references throughout the game. It's fine to just take stuff at face value but the lore is there and really legit.)
Anyway, back to Garleans. What I'd argue is that while they do believe in primals, they don't believe in actual gods as higher powers as per Gaius van Baelsar's massive rant on the subject in the Praetorium. He seriously does not understand what makes primals any different from gods. To his mind there is no difference. He recognizes that the idolatry of primals is dangerous literally, psychologically, and culturally. He can't understand what keeps the Warrior of Light or Eorzeans as a whole from becoming hypocrites who are no different from the beast tribes whose primals they slay. Ysayle's summoning of the false-Shiva and Ilberd's invocation of Rhalgr both further highlight that the humanoid races are no less capable of this form of idolatry compared to the beast tribes as well.
However, what Gaius misses is that it is possible to separate the divine concept from the symbol used to invoke it. I'd actually like to draw attention not only to Hydaelyn's representation as a crystal, but the fact that when Louisoix flashes back to his own invocation of the Twelve in the Unending Coil of Bahamut? All of them were crystals too. This is notable because while across Eorzea there are humanoid representations of the Twelve, none of these were utilized in this scene. I'd like to invite the possibility that we as viewers see crystals specifically because they are strange, non-humanoid, alien, and symbolize something beyond mortal comprehension. Hydaelyn is the name of the world itself as well as the Mother Goddess the WoL communes with. The crystal and how she speaks are placeholders for the very planet, and similarly when Louisoix calls upon the Twelve he is invoking life and death, navigation, fertility, destruction, industry, love, exploration, fate, etc. These concepts are not things that can be visualized in any literal sense, but they remain real nonetheless and so we are shown crystals as placeholders for them too. Gaius, however, wouldn't be able to understand the crystals as symbolic placeholders and would instead see Louisoix, the WoL, and Eorzeans in-general as a bunch of crystal-worshipping hippies if he saw that same scene.
That, I think, is the issue Garleans run into. I don't think they're capable of symbolic thought and operate on a purely literal basis. This might also be why they can't use magic. However, since primals by nature use literal thought rather than symbolic it then becomes a question of whether or not Garleans are capable of faith or belief in something, rather than belief in any divine concept. Given that Nael van Darnus was able to be enthralled and that Garleans regularly invoke the Emperor in the way non-Garleans would invoke a deity, I'd argue that if anything the lack of symbolic thought makes Garleans more likely to summon a primal rather than less. The purely literal thinking of Garlean atheism is just another flavor of the purely literal thinking that goes into primal-worshipping fundamentalists.
I'd also like to invite two questions about how and why the Resonant work, and whether that quality worked on Zenos specifically because he has Ascian blood (if he does, this is a question of whether Solus actually literally made babies with some Garlean chick or not and how that would even work) or if his soul was artificially altered to allow symbolic thought. I don't think his merging with Shinryu was because of his becoming Resonant, but I really wonder if his being given room to experience the perceptions of others and being forced to understand life on a much bigger scale/beyond himself will change him as per Fordola. I seriously think the guy had something like antisocial personality disorder going on with his characterization so whatever follows in his development could get real interesting.
I absolutely think there's a risk of the WoL becoming a primal vessel down the line though, and honestly as a reference to Shougun's thread about a possible dark transformation job... I think something along those lines could be a real possibility if that happens. Agree I don't think it'll be in Shadowbringers, but my god if/when it happens we are in for a wild ride.