Axel Springer says that ad blockers threaten its revenue generation model and frames website execution inside web browsers as a copyright violation.
This is grounded in the assertion that a website’s HTML/CSS is a protected computer program that an ad blocker intervenes in the in-memory execution structures (DOM, CSSOM, rendering tree), this constituting unlawful reproduction and modification.
I wouldn't worry if that's their argument: you can modify whatever copyright-protected work you wish as long as you don't redistribute it, otherwise taking notes in books or using an equalizer when listening to music would be copyright violations. Surely you can do the same with the programs you run on your computer (also regarding computer programs, live patching is a thing).
That said, copyright law has been so absurdly twisted and stretched (suffice to say it was born to protect authors and it now protects megacorporations' profits) that it's worth to keep an eye on this.
PS: You may want to take a look at Axel Springer's newspapers/brands