It appears that only part of the Makeshift scarf gets re-textured when a shader is active, but the back half of it remains white. This bug is also present in the Character menu.
-Sorry about the image quality, took it from my phone
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Nope. Sadly that's always like that. Not a bug. The back remains white with every shader. It doesn't change. Similar to the trim in the hood for the dust walker cloak and how all rare cloaks have a white tint to them. So this isn't a bug. Just how the scarf is. 👌🏻