Glass petri dish to replace plastic petri dish?
Glass labware is usually made of borosilicate glass which is resistant to temperature changes, so putting a glass petri dish in a -20°C freezer should not be problematic, at least with respect to glass cracking because of temperature changes. I think the warning on your freezer is probably meant to warn against closed glass containers filled with liquid; as water freezes it expands and may mechanically break the glass, but for a petri dish is should not be an issue.

I would be more cautious about heat shocks with a -80°C freezer, though; in my experience at that temperature there is still a risk if the glass is not of good quality.

On a side note, depending on what you use the petri dish for, the surface chemistry  may be different from the polystyrene of plastic petri dishes, and if you are growing cells directly in contact with the surface, switching to glass may change their behavior.