The Far God Cult were introduced on GalNet some time before the current arc of GalNet. They were heavily persecuted for their beliefs, with at least one politician accusing them of being Thargoid spies and encouraging attacks against them. The end result of that particular storyline was that they mostly went into hiding and that the claims of them being spies were debunked. They are ordinary people and not in a position to be the NMLA's benefactors. Similarly to the Marlinists however, their persecution is now being exploited by Theta-7 to avoid detection by hiding amongst them.
There are a couple of practical requirements for the NMLA's benefactor that we can figure out from the NMLA's actions and capabilities.
1) High level of security access in the Empire. This is evidenced by the assassination of Harold Duval, as his travel plans should have been a close secret, as well as the prison break of Serene Harbour, which was explicitly mentioned as requiring top-level security codes with Imperial Intelligence.
2) Access to Thargoid enzymes. There is not a great deal of lore on the process of gathering these but, unless we are to point the finger at Aegis, this probably comes down to simply being very well funded which is a requirement anyway due to the scope of the NMLA's activities. The NMLA were also only a small-scale group before they had access to this funding.
3) Able to bypass security in all three superpowers to bomb the capitals. Not much practical info on how they did this, but it suggests the involvement of the Club, as few other candidates span multiple superpowers in this way.
Neither the Far God Cult nor Hadrian match these requirements. Hadrian in particular has a number of other factors that suggest he isn't the benefactor even if he theoretically could - he's been fighting the NMLA, his political stance is the opposite of Marlinism, he's a Duval, he's been shot by them, he's been bombed by them, they've tried to frame him as the leader of their Duval-killing group after he helped defeat a group of them...
My guess is that the benefactor is Chancellor Blaine, possibly working with Senator Scordato. He has the access required and has connections to multiple assassination attempts on the previous Emperor.
I've previously written another post on this, which also has links and evidence for the rest of this post.