It's true: I see the world in physics. You might, too. So when I saw a thing at Panera Bread, I spun it into a narrative that's too good to verify. Meaning I could have it a bit wrong, but it feels right. It's 2019, so... good enough.
In any case, here's the observation: an LCD screen in portrait orientation goes dark when viewed through polarized sunglasses. Unless you tilt your head sideways!
My story is that the LCD was manufactured to be used in landscape orientation, as is the case for 99.9% of such displays. In that orientation, the polarization inherent in LCDs was set to be viewable even through polarized sunglasses. But the Panera queue application required portrait mode. Hence the trouble.
And honestly, if you're indoors at Panera, why are you wearing your sunglasses? (Actually, if they're prescription, keeping them on while waiting for your coffee might not be so unreasonable.)
Note that your modern smartphone can be viewed in portrait or landscape through polarized sunglasses. Their displays have been depolarized! Some kind of sorcery is at work here.