There's a smell of stale fear that's reeking from our skins
The way this fear is described makes it feel like it’s suppressed. And it is described as coming from “our” (i.e. everyone’s) skin, not just the narrator.
The type of fear that he is talking about here is the fear that life really is just one long, pointless experience that ends in death. Even the devoutly religious who have almost no doubt that living life the right way will lead them to heaven have to suppress these fears in order to keep living the way they are. They are only human after all.
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