Navigation data is important, which is why it's required to be refreshed within 28 days (this was a big worry during the recent Garmin outage BTW), but whether it's critical depends on often domain-specific definitions. AFAIK it doesn't meet that standard by either software or aviation standards. Also, it's definitely not software, so "critical software updates" is still incorrect.
On an airliner that can land in cat III approaches (ultra low visibility down below 100') then this data is critical since it's used in automated systems to help land the plane.
It's going to be required to fly legally, without a waiver. But in terms of the engineering development assurance required, typically it is more 'critical' than radios and less so than flight controls, engine controls or displays. Of course this depends on the safety analysis performed for the individual aircraft and intended operations.
