The Faceless Men are fascinating to me because they seem to have a unified theory of the afterlife.
No they don't. There is literally no textual evidence for this.
If such an afterlife does exist, then the Faceless Men become the natural expository vessel for us to learn about it.
This is also a weird misreading of the Faceless Men. We have evidence that remnants of a person or a life can remain. The Weirwood trees are one such instance of preserving consciousness. Also there are skinchangers who can leave part of themselves in animals. It's also possible that the Others have a version of preserved consciousness. Also the Undying.
That's not what the Faceless Men do. In fact, they seem fundamentally opposed to such preservation. For example, Braavos and Qarth are fundamentally opposite places. One is a fre city, the other is a slave city. So the FM probably would not have a very positive view of the Undying of Qarth.
They are...with the living. What happens after they die?
Yikes buddy. GRRM is an atheist. He belies that nothing happens when you die. In ASOIAF he has certain structures within nature that preserve echoes of consciousness, but this isn't the same as an afterlife. The Faceless Men don't have an afterlife.
But what happens if a weirwood isn't present? What happens if the person isn't a telepath?
Have you considered nothing? That their soul just dissipates? If everyone survives somewhere then there is no point to the Second life. The whole point of the Second Life is that Wargs are able to magically preserve themselves by projecting their consciousness elsewhere. That's a special thing that wargs can do. But even wargs slowly recede into the animal until they are just a presence.
Dany has a number of magical figures/institutions seemingly backing her (Quaithe, the Red Priests, etc.).
Also Dany is magic.
Bloodraven is hell-bent on preventing a Blackfyre from ascending to the Iron Throne.
There is no evidence BR still gives a shit about Blackfyres.
Melisandre was trying to help Stannis win the throne
Yes...
as seemingly is the Iron Bank.
They're a capitalist institution. Not a magic cult.
In the middle of it all stands Varys, subtly sowing chaos and manipulating events towards his own chosen champion, (f)Aegon. His outsized influence in these events make it seem odd for him to be a mundane figure when all the rest are magical. Odd either because he's NOT mundane, or odd because his mundanity is important to his identity and his objectives (i.e. he is knowingly trying to fuck with the plans of all of these demi-gods).
It's quite clear that Varys hates magic. The show has fucking pounded this into every key Varys scene. To still expect Varys to be a practitioner of magic is willful ignorance at this point.
It doesn't mean he is doing more to directly influence events compared to the Shrouded Lord.
Yes it fucking does.
So far all we know for certain that Bloodraven's done is talk to Bran and Euron telepathically, maybe manipulated Melisandre, sent Coldhands around to do some stuff, and subtly intervened through Mormont's raven. If the Shrouded Lord triggers a Westerosi greyscale epidemic then that's a WAY more powerful intervention than Bloodraven, and wouldn't need additional POV resources to introduce. So is if the Faceless Men reveal themselves (at least to readers) and start killing key political figures.
Are you even serious right now?