I repeated the measurement reported in entry 1055. I did the whole turn of the rotational mount.
The noise doesn't show a clear dependence on the polarization angle.
I also plot the DC, and we can see a periodical (4 periods in 360deg) fluctuation of the laser intensity of 3% peak to peak. This shows that even if the optics are nominally non-polarizing, they still have some small polarizing effects.