I don't believe the windshield is polarized. On the other hand a HUD is produced by reflecting a projection off the windshield.
All reflected light is polarized! Unfortunately it's polarization angle is rotated 90 degrees to most polarized sunglasses. That's why rotating your head over rotates your polarized glasses into the polarization plane of the reflected HUD light and why it gets brighter.
I use polarized glass prescription sunglasses so I specifically didn't order the HUD option when I bought my BMW 4 last year. There doesn't appear to be an option to get polarized sunglasses with their polarization rotated 90 degrees. But then maybe if there were they might not work to reduce sun glare, and possibly you also wouldn't be able read digital watches.
