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It seems like Gimp is not rotating correctly.
I have two duplicate layers of this GIF: 
It looks like this:
I click the rotate tools, click one of the layers, and choose 90 degrees. It looks like this:
Then I click the rotate button to apply the rotation, and I see this:
The rotation is off. Does anyone know what is happening here?
The general fix to any anti-aliasing problems when rotating 90° is to use the Layer>Transform>Rotate 90° commands instead of the free rotation tools.
Per the GIMP docs:
The Rotate 90° clockwise command rotates the active layer by 90° around the center of the layer, with no loss of pixel data. The shape of the layer is not altered, but the rotation may cause the layer to extend beyond the bounds of the image.
Using the fixed 90° rotation commands in Layer>Transform>Rotate will always give you a sharp result (since they just move pixels around; they don't actually perform any anti-aliasing or interpolation).
I haven't been able to recreate this issue using the normal rotate tool, so I'm not quite sure what the cause of the issue is, but this should resolve it regardless. Hope it helps!
You say you have "two duplicated layers". By default, the rotate tool will do its thing only on the active layer. For all I can tell, the bottom image is the result of your rotation applied to one layer, and the other layer unchanged, stacked on top of each other.
Just use the Layer's dialog (ctrl + L) to toggle the visibility of your layers and
check the result.
