[Artmasterx]

If you think of light as a having two axes, and x-axis and a y-axis, then a polarizing filter (sunglasses) will generally removed most of the light in one of the axes. So after the filter you are left with light in only one of the two dimensions (and typically 50% of the initial light intensity). If you then run the polarized light through another polarizing filter at 90 degree angle to the first, all light will be blocked (if the filter is at the same angle, no light will be blocked).

You can test this by taking two pairs of polarized sunglasses, lining up the lenses of the two, and then rotating the sunglasses relative to each other so you see through one lens of each pair. At some angle, they will block most or all of the light. The first blocks light along one axis, the second blocks it along the other.

The reason that polarized sunglasses essentially negate the HUD is because the reflected light is mostly polarized. The reflected light coming from the HUD is polarized orthogonal/opposite to the sunglasses, so that light is completely removed by the sunglasses (unlike most other ambient light which is not polarized, of which only a portion of the light is removed by the polarization and tint). If you tilt your head sideways 90 degrees, I bet the HUD shows back up because now you are aligning the axis of the polarized sunglasses with how the reflected light is already polarized. This is the same with the radio displays, where if you tilt your head you can see it again.

The reason that putting something like transparency film (oriented correctly) over the radio display helps is that it changes the angle of polarization so that the sunglasses don't filter all the light anymore.

My guess is that all polarized sunglasses are designed with the same axis of polarization because most reflected light (i.e. of the water, etc) is not what we want to see and is usually polarized the same way... so sunglass manufacturers choose the polarization axis to kill those types of light.

Anyway, not the most eloquent, and maybe not completely correct, but the general idea should be about right.