@dejudicibus:
WP 4.9.6 was released yesterday makes the first steps WP being GDPR compliant by letting you define a “Privacy Policy” page (they even included a sample text that is good enough to let you understand what exact data you have to include). WP core even delivers a “Personal Data Export” and “Personal Data Deletion” tool. However on the frontend there is simply no means for the user to inquire any activity from the administrator. So you just need to include an email address in the privacy policy page where users can submit such requests. Maybe you even can setup a contact forms for these purposes.
Being told all that it is obvious that WP has just began with the first steps and there are quite a few to be done if in the future. The most complete GDPR solutions this day seems to be: GDPR plugin