GDPR simply classifies "personal data" as any piece of information that can be used to identify an individual. A static IP used by one person could therefore be considered personal data while a public IP shared between thousands of people behind carrier-grade NAT would not.
The problem is that you can't tell the two apart and decide when it's safe handle the IP.
Indeed. My dynamically allocated public IPv4 address, given to me by my cable company, has been the same for as long as I've lived here, over four years now.
Ironically, my IPv6 prefix can change several times a day...