You may use it for other things, but that means you are going to use it for something that it wasn't intended to. The result may not be exactly nice, and I doubt people that are used to Civ V can shake off the idea that they are spreading religions in spite of what the text and UI will say.
It frankly doesn't matter what a system was intended for, if it fits with the new package perfectly (and it definitely does for cults, mega-corporations as well if you don't employ "faith" as a resource and stick with manipulating other factors), the fact that it was originally meant to portray religions is irrelevant.
As for Civ5 players being used to spreading religion, I actually see that as a strength: it would allow for immediate contrast between organized religions and whatever the new system represents. The worst it will do is make people think and reflect on whether what they like and dislike about religions is [only] inherent to organized religions or is a mutable property that can extend to other concepts as well.
The Datalinks are pretty clear at defining "fundamentalism" as "religious fundamentalism"
<snip>
Yes and no. It's true that the social policy itself does not mention Atheism, However the Faction Profile of Sheng-Ji Yang reports as his agenda "Atheist Police State".
Moreover Democracy and Police State are mutually exclusive to Fundamentalism and if you adopt the latter the factions that adopted the formers will tell you
<snip>
I'd say the last bit depends on the leader: it would be more along the lines of, "We've had separation of church and state for over 500 years now, yet you've decided to regress?" for Lal and Deidre, with room for interpretation for others (I'm mainly thinking of Morgan, Santiago, Pirates, Caretakers, and Usurpers). Otherwise, I stand corrected.
[Would you] say that the <snip> fervor with which the world has embraced neoliberal economics <snip> was a type of fundamentalism?
First of all, quoting Wikipedia is never a good thing (not a reliable source, I can easily just modify a quoted passage to suit my argument). Arguing about a definition is pointless, since definitions are strictly a medium for concepts and ideas; unless some of the parties understand a vital word/phrase differently from the rest, debating definitions only serves to make one party feel self-righteous, it doesn't actually do anything constructive (ie. help advance the evolution, expansion, and/or adoption of concepts and ideas).
The <snip>'s are meant to help focus on constructive paths and avoid turning the thread into a toxic waste dump of unwavering hatred; my apologies if you feel insulted.
In any case, the [internal] definition I use (emphasis: in my head, not necessarily the widespread definition) for fundamentalism is abstracted from organized religion: it's a sort of effort to shift the implementation of an idea towards a "pure", literal form. Since the "purity" of the implementation is paramount, all other ideas would be subservient.
As a result, if by "neoliberal economics", you meant "neoclassical economics", then no, I wouldn't say the adoption of its tenants in the English-speaking world has been fundamentalist: for example, pretty much all governments still subsidize some economic sectors (usually agriculture, transportation, and energy), whereas "pure" neoclassical economics leaves no room for subsidization.
