Saying faith in “anything” can “make magic” is oversimplification. If someone has faith that chicken soup is good for the body and soul, that doesn’t mean it can do healing magic and redeem sinners. There has to be something substantive to believe in…whether religious doctrine/dogma, a philosophical stance/pretext, etc.
An instance of non-religious, philosophically based “faith” could come from a deep and abiding faith in the principles of Plato’s Republic. The American Founders used a lot of that to make a nation out of nothing and it’s still standing (however battered and time-worn). There’s plenty within Plato’s treatise to found a faith-based system of beliefs that could well rival those of any religious organization in the world. Likewise, Marx’s Manifesto contains ample dogmatic/doctrinal tenets for the same. Whether or not a particular form of communism acknowledges religion or not isn’t germane. Does the philosophy of Communism lend towards faith? Ask the Bolsheviks whether their faith was good enough…
Heck, for that matter, Sun Tzu’s (circa 500 B.C.) “Ancient Art of War” could match them. After all, doesn’t Bushido (“Way of the Warrior”, code of conduct adhered to by samurai) embrace every last scrap of the essential nature of Ancient Art of War and still qualify as a non-“religious” faith? Even Musashi’s “Five Rings”, a central piece of Bushido training literature since the 1600’s, is part of Bushido now; sort of a Bushido “New Testament”. The seven “virtues” of Bushido are Rectitude, Courage, Benevolence, Respect, Honesty, Honor, and Loyalty… certainly a match for Chastity, Temperance, Diligence, Charity, Patience, Kindness, and Humility the seven Virtues of Christianity. A strong enough belief in Bushido might well convey religious level faith “magic”.
I think it comes down to, what does a one believe in… presuppositionally... without need of proof. That’s the nature of faith.
Duct Tape, peanut butter sandwiches and Sharon Osbournes aside, if there’s something substantive to the belief system, there’s substance for enough faith which, in game terms, will translate to a “True Believer” faith-based character. That’s all the GM needs. Getting the players to swallow it might be another story, but as long as the GM deems it good, it is good.