Whether you parse log files locally, or in the cloud, or use a cookie really doesn't matter to the GDPR. They only mention the word "cookie" once in the entire law, it's independent of technology, as it should be. If you store personal information (like IP address) in your log files, you still need consent.
There is no cookie law. There was a privacy directive 7 years earlier, but it did not have any fines associated with it so no one really cared. We are discussing the GDPR that superseded the GDPR.