Navigation is not critical? It seems like a pretty dangerous turn of events to try a low-visibility landing based on outdated navigation data.

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.

The headline is misleading in my view because loading navigational data is not the same as an update to the software code or operating system.

No no, the old airplanes have a binder full of floppies so that any time the plane has wheels on ground, you can reload one of the critical systems without waiting for someone to fly in with replacements.

By the 787 they were working to replace this all with code signing.

ETA: This bears repeating: aircraft have interlocks. There is a sensor that tells you that the plane is parked (wheels on ground) and there are connections, maintenance, and administrative changes that cannot be made unless this is the case.

Nobody is going replace the maps with Rick Astley somewhere over the Pacific at 3 am.