When websites use IP addresses as an authentication factor because they change so infrequently that it's when it does it's hard to argue that you can't identify users by the source of their traffic.
Plus the addresses themselves betray personal information. If you use my service I can know a great deal about you by your source addresses.
* You shop at Target, but sometimes Wal Mart when you're in a rush.
* You get coffee at the Starbucks on 5th every morning.
* You live on 2365 Chestnut Dr.
* I know where all your friends live and how often you visit them.
* You used to go to this one apartment a lot late at night, but not anymore. How are you dealing with the breakup?
* You work in the office building on Main.
* You went to a Mercedes dealership. You deserve it after all emotional stress you've been though.
* You went to a fancy restaurant yesterday, date night?
* You're coming from a couples retreat in Cali, I'm so happy for you! Getting back out there.
Example: you run a website and in your log file you only collect IP addresses, apparently anonymous. Log lines come with a timestamp. You now know that a user at IP X visited your website at time Y. Sounds like this should be personal information in my opinion, and that log file should be protected.
https://www.whitecase.com/publications/alert/court-confirms-...
A first and last name is also insufficient to identify a person, are you going to argue that names aren't personal?