New EU-DSGVO 2018 - Is a new agreement necessary?
I do not think there will be an easy answer to this GDPR question (also it is only party CiviCRM-related) but the following resources could be useful:


https://www.fellowshipproductions.co.uk/make-your-website-gdpr-compliant/
https://en.wikipedia.org/wiki/General_Data_Protection_Regulation
https://www.gdd.de/gdd-arbeitshilfen/praxishilfen-ds-gvo/praxishilfen-ds-gvo
(coherent information in German lanaguage)


Also, you will be happy to know that there is a CiviCRM extension which focusses on the topic of GDPR / DSGVO: https://civicrm.org/blog/parvez/announcing-a-new-gdpr-extension