... and other devices too. However, many LCD displays have implemented the polarization differently and there is no issue at all unless you tilt your head sideways.

Polarized glasses always orient the polarization filters to the horizontal plane (with your head in normal upright position) and newer LCD displays do the same. You will see this effect if you look through a pair of polarized glasses while wearing another pair of polarized glasses, and rotate the one you're holding. The light through the glasses you're holding will be totally blocked when they're oriented perpendicular to each other, and less will be blocked as you move them to a different rotation orientation.

Bottom line, get a different CP or (as others have said) don't use polarized glasses. Neither my Lowrance or my Garmin have this issue, but those are older models. Before you buy a new CP it would be good to check them in a store or boat show.