I can give you general information about what’s to come in upcoming versions of WordPress and Event Espresso 4 with regards to the GDPR:
Event Espresso will introduce tools to assist with GDPR compliance starting with version 4.9.62. Information about each of these tools is currently available on Github (more information will be published after official release of 4.9.62)
These tools will work along with the tools that WordPress will introduce starting with WordPress 4.9.6 (currently in beta). As with any other legal requirement, it is up to the site owner to take the steps required to be compliant with the GDPR and any local variations that may be introduced.