So, we've seen the term fedora bandied about here frequently, but what exactly does the term entail?
We can be sure that the term has expanded past its origins as an appeal to style meant to shame atheists into silence, as it's used quite frequently in subjects not even remotely related to religion (art for instance). So we must look at the deeper traits of the idea, the basic patterns of behavior that were being mocked. Because although it was used to mock atheists in general, it did so by evoking a very specific stereotype of them; this being most observable in that iconic quote about being enlightened by one's own intelligence.
I look at the term, and I see within it a commentary on a deeper, and more pervasive pattern common among social awkward young men (though perhaps not exclusive to them). The sorts who have little social success and consider themselves to be above-average in their own intelligence. This behavior can be observed in a sort of "matter-of-fact," "common-sense," evaluation of things that refuses to consider the deeper, and ephemeral natures of things, and automatically considers a different perspective than their own to be borne of idiocy. The "fedora" has in their mind done all the growing they need to do, has shit figured out, and is now set to fix the rest of the world.
We see this among some atheists, in which they refuse to accept that the reasons for belief people experience feel very real to them and are not just wishful thinking or stupidity (to be fair, we see this with many Christians here as well, when it comes to other religions). We see this in art threads when they trot out Ilya Repin's famous work and refuse to consider that beauty does not mean strictly "pretty pictures" (or harmonious if they're particularly well-spoken) or that skill does not have to go into creating photorealism.