Every pair of polarized sunglasses are vertically polarized. They have to be to block horizontal reflected light. Cool trick — next time you see a good, bright rainbow grab a pair of polarized sunglasses, and tilt your head at random angles while looking at it.
LCD panels are also all polarized, but they don't have to be vertically polarized because they aren't blocking reflection from flat surfaces like a wet road of the water. If the polarization angle on your LCD matches the angle on your glasses, you won't see anything.
Older LCD's had fewer problems, because TN panels are polarized at 45 and 135 degrees. They need to be because of the shape of the crystals in a TN panel. They're asymmetric, and you need to polarize at 45 and 135 to provide enough contrast and the maximum viewing angle. If you've ever used a wide TN display you'll notice that things start to look weird if you're not directly facing it. It would be even worse if the polarization angle was wider or more shallow.
Most modern high-res LCDs use IPS or PLS panels. They will display a better viewing angle if the polarization is at 90 degrees or zero degrees. Some use a backlighting pattern that requires a zero angle (vertical) polarization to display higher contrast and "blacker" blacks. Others use a different backlighting panel that needs 90 degree (horizontal) polarization so that the blacks don't "glow" if you're not viewing straight on.
This is why older panels can look fine when held vertical and horizontal, and newer panels are unreadable in one direction.
None of this helps if you can't see your phone when you're holding it the way you wanna hold it, but I thought some might find the way it works and why some are different than others interesting.