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I think HUDs are inherently invisible to most polarized sunglasses. Polarized sunglasses are made to filter glare and reflections. The act of reflecting (am not a physicist so don’t know the exact mechanism) reorients light waves into a horizontal plane, so all reflections (and glare, which is a type of reflection) is horizontally oriented. Polarized sunglasses filter out horizontally oriented light, that is how they cut down on reflections and glare. Since the HUD image is effectively a reflection of the HUD screen off the windshield and thus becomes horizontally oriented, then polarized sunglasses will filter out the HUD.
Simply put, the point of polarizing sunglasses is to filter out reflections, and HUD image is a reflection.
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