Why is this? I know that polarized lenses cause weird problems with
LCD panels, but how do polarized lenses make the aircraft instruments
harder to see?

Some of the instruments have polarised glass themselves. Some glass will
reflect polarised light at certain angles. Some angles of flight will cause
the windows of the aircraft to admit polarised light into the aircraft. If
the two lens are lined up in front of each other, the result is the same as
when you hold up two pairs of polarised sunglasses and look through both.
Rotate one of the pairs through 360 degrees and watch what you see. At
certain angles they will almost totally block the view. This causes the
affected instrument face to go black.

When you are trying to read your instruments with the sun at the same angle
as your instruments, you don't want to loose your view of the air speed
indicator!

Hope this helps,
Peter