No, it's the nature of polarization.
Go outside tomorrow with your polarized glasses on. Look at a static scene like a parking lot.
Tilt your head left and right. You will quite clearly see the intensity of the glare go up and down. Or just hold your sunglasses out in front of your face and rotate them about the center. You will see the image appreciably change.
It's just the nature of polarized light. The glare is primarily in a single polarization range. As you rotate the polarized lenses against the glare's polarization, the amount of glare getting through goes up and down.
If you ever use a polarizing filter on a camera you will see the same effect. These filters are assembled so that you can swivel them while they're mounted. As you twist the filter you will see the glare level go up and down.
You can see a great demonstration of this here:
This is someone filming while rotating the polarizing filter. This is the exact same effect you see as you tilt your head left and right while wearing polarizing sunglasses. Maybe most people don't notice it specifically, but this is what you're experiencing when you get "reduced depth perception" or whatever.