That's the standard story, but it's not the whole story. Specular reflections do preserve polarization, but they also redirect the ray. Polarization is preserved with respect to the ray direction and the surface orientation, but the absolute direction of polarization is changed. If the redirected ray is then specularly reflected off another surface, the same thing happens. Depending on how the surfaces are oriented, you can end up with multi-bounce rays coming toward the lens with the polarization rotated to any angle at all. If the surfaces are oriented randomly, then the polarizations are random also.Specular reflections preserve polarization, but diffuse reflection does not.
I can illustrate this effect using a very simple scene consisting of two shiny steel balls, mostly illuminated from the right side by polarized light. There's another polarizer on the camera lens.
Here is an image of the scene, with and without annotations.
In the annotated version, I've drawn blue boxes around the primary one-bounce specular reflections. Then I've drawn red boxes around the primary two-bounce specular reflections. These two-bounce reflections are caused by light bouncing sideways off one ball, striking the other ball about half-way up the hemisphere facing the camera, and being reflected up into the camera.
Now, by rotating the polarizer on the camera lens, I can arrange to kill the primary one-bounce reflections, or the upper two-bounce reflection, or the lower two-bounce reflection, but there's no way that I can kill even two of them at the same time!
Here are those three cases, first as single frames and then as a continuous animation.
I'll let you work out the details of how things get rotated. I find them quite difficult to explain even to myself, let alone to anybody else. The point is just that multiple bounces can cause the angle of polarization to rotate.
I think this is not the same phenomenon as the usual distinction in which surface reflections retain the polarization of the illumination but subsurface reflections resulting from absorption and re-emission do not. Certainly there's nothing in this scene except for specular reflecting spheres, plus some miscellaneous stuff like balsa sheets in the environment around them that we're ignoring.
This posting was prompted by the discussion about diatoms and cross-polarization, HERE. I initially posted this as a reply there, but then decided it would be more generally useful as a separate thread.