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!