It's mostly incidental, because Square has always referenced religions and mythologies throughout the Final Fantasy series. By setting up conflicts between what they reference, they incidentally recreate some of the old myths' conflicts. Gnostic ones, Zoroastrian ones, Juedo-Christian ones, Islamic ones, and the list goes on and on.
The idea has been floated in several places that Hydaelyn is similar to:
- Satan / Lucifer / Azazil
- The Demiurge / Sophia
- God / Yahweh
- Morgoth / Melkor
There's also a prevailing idea from a bunch of Youtube "philosophers" that Square Enix RPGs almost always reference Gnosticism and The Demiurge, and that what the player fights as god at the end is actually just their take on The Demiurge.
These assumptions almost always ignore all context surrounding each character, and their literal actions often being at odds with what any of those mythical figures would do.
For instance, part of Lucifer/Azazil's story is that he was an angel made from a different substance than the other angels. Sometimes he is the first angel. Other times he is the last. As Azazil (islam) he was made from, "toxic flames." His fall was caused by his refusal to bow to God's new creation, Mankind. A similarity he does share with Hydaelyn is the proclamation of his own divinity, and having to share the lower world with man.
A lot of players just assumed Hydaelyn to basically be the setting's true God, even after it was revealed she was man made in Shadowbringers.
The Demiurge / Sophia comparisons have come into the light recently since Endwalker analysis is still going strong. She doesn't really fit for Sophia at all, though, since Hydaelyn is not a First Principle, and she also doesn't create much of anything other than, I guess, The Twelve. And The Twelve don't really fit in as the Demiurge at all, so it's kinda ehhh? But Hydaelyn as The Demiurge sort of fits better, since it also creates, but its creations are material rather than divine, and it creates life and stewards for it, called Archons. The Archons keep the material realm from ascending back to their divine roots. Now, often, The Demiurge takes the name of different Satan analogues when people tried to mix Gnosticism with Christianity or other religious ideas, but that's not really a 1 for 1 either.
Of course, just because there isn't a 1 for 1 match up, doesn't mean it's not what was intended.
We might not want to think of the developers as Gnostics, Satanists, Christians, or any other flavor of religion, but they very well might be any of those things. Ever since the early 2000s really got Atheist and Agnostic ideas flowing really broadly into society, there have been pop-ups of things like Satanists that do it more to rabble rouse, but there are true believers out there, that believe their own doctrine to be just, because they based it off of actual good morality they were taught or learned from others, merely applying the name / deific figure they want to it, as to stand contrary to spiritual belief they themselves hate. And these old lost religions and spiritual beliefs get dredged up into it, too, because they seem more fantastical and like a hidden truth that makes folks who read about it feel special, I guess.
Like, it could be, that the devs at Square are Gnostics that have a positive view of Sophia and The Demiurge, and they wanted to proliferate that in spirit, if not in doctrine, by putting a positive spin on the idea by writing Hydaelyn the way they did.
Didn't think you'd read anything wackier than an RPG plot today, did ya? But this is the kind of stuff that is an RPG setting's inspiration. Its bread and butter... or perhaps its Communion wafer.