Here's the kicker - most European online publications were already in compliance. GPDR is only slightly more stringent, than most EU privacy laws on file.
The biggest complaints come from foreigners, if you haven't noticed.
No one knows if they are in compliance or not yet. For instance https://www.bankinfosecurity.com/fresh-gdpr-complaints-take-... outlines a complaint that all of real time bidding that is compliant with the IAB compliance framework is not compliant with GDPR.
Major publications, for instance Der Spiegel, which are trying to be compliant by following that standard (and they had to do major work to do so) may find they are out of compliance http://www.spiegel.de/extra/what-we-do-with-your-data-a-1211...
Similar complaints have been brought against publishers that used googles compliance framework.