Why do my new sunglasses make my iPhone and iPad look funny?
It seems it's not EVERY phone or iPad - have you tried taking our device to the Apple Store and asking them?  (Yeah, I know, it's not always convenient and if you do, make sure you make a Genius Bar appointment ahead of time so you don't have to wait).

Take a look at this page:
http://www.phonearena.com/news/iPads-and-polarized-sunglasses-dont-mix_id28909

I can't seem to find why the problem occurs - it seems to be something about polarization needs to be at 45 degrees:
Why are LCD Panels Polarized at 45 degrees