Put your polarized sunglasses on, look at your LCD monitor, and tilt your head. (Or, for less neck stress, just hold the glasses in front of you and rotate them.) At certain angles, the display should be completely black. This is because most LCDs, without some sort of filter, emit polarized light. When the orientation relative to a filter - your sunglasses - is correct, the light just bounces off. All reflectance, no transmission. 3D TVs and movie theaters rely on this phenomenon to present different images to each eye.
I also notice this with ATMs, gas pump screens, and the like.
Not all displays have this issue - for instance, I can read my iPhone 6's display with my sunglasses on regardless of orientation.
So, to answer your question: whether or not this is a problem depends on the display technology and filters in play. These days, I expect the automotive designers to take into account that most "nicer" sunglasses are polarized, so they'd either orient the panel so that you'd have to be rotated 90* to have an issue - assuming, of course, that the glasses manufacturer consistently puts the "correct" side of the lens at the top of the frame, or that they would apply some sort of depolarizing coating to the display. If I were wearing my Ray-ban's while driving the wife's Caddy and I couldn't read that nav screen, I'd be nonplussed.
