It looks like I found the problem! I still don’t understand why I would get those flipped normals at all, but I think I fixed them. First I replaced the WorldAlignedTexture-node with WorldAlignedNormal. Don’t know if that one is new or I just didn’t find it the first time. Then I still had problems getting it to look right. While messing with settings related to “tangent space”-normals versus “world space”-normals and stuff, I disconnected the VertexNormalWS-input from the WorldAlignedNormal-node by chance, which finally did the trick. Again, I have no idea why the diffuse texture node would require a vertex normal input and the normal texture node doesn’t. I have no idea why any of this would have something to do with overlapping polygons either, but what the hell. Glitches are gone.