I got back to my books, and found that I was remembering a bit incorrectly; Doubting Thomas is usually just a flaw.
In the Weird War setting, however, they have this version:
Doubting Thomas (Major)
Besides the description presented in Savage Worlds, Doubting
Thomases are just not prepared to deal with the things that make
Weird Wars...weird. Characters with this Hindrance suffer double
Sanity loss when such an event occurs. On the plus side, they start
with a Sanity of +2 for their stubborn faith in the mundane.
Anyway, just a thought for something that could be built on.
I think that in my games I will be taking the angle that, whatever they are or represent, the Icons don't care whether anyone believes in them... but the idea that someone, who not only doesn't believe (I know plenty of non-believers who have superstitions or casually use the religious language of their culture/family's religion) but insists on strictly enforcing a materialist point of view, could cut themselves off from benefiting from that attention? Is interesting.