Most web hosting companies ​are be holding data of clients ​as WordPress very often captures email address, and other visitors information.
Some Hosting companies have announced their plans to reach GDPR compliance before the May 25th 2018 deadline. But searching googles yields very often no results for a lot of hosts. From the time of writing, Siteground and wpengine seems to be the ones that are working to reach compliance the most among managed WordPress Hosting companies.
​Here's a list of announcements made by website hosts regarding GDPR Compliance.
Managed WordPress Hosts
(or with some WordPress specific plans)
​Siteground
Status :​ GDPR COMPLIANT (​May 24th 2018)
See latest post : SiteGround is now GDPR Compliant May 24th 2018
​Previous news :
https://www.siteground.com/blog/gdpr-siteground-getting-ready/
Webinar May 10th 2018
​What is GDPR and what is your web host's role in it
WPENGINE
Status : IN PROGRESS (April 10th, 2018)
See their latest news :
https://wpengine.com/support/gdpr-compliance/
May 10th 2018
New Service Level Agreements, New Terms of Service, New AUP, DPA, Privacy Policy
WPX Hosting (Traffic Planet)
Status : Unknown
See their latest news :
Only general information is posted here:
https://wpxhosting.com/knowledgebase/article/147/what-is-the-eu-s-general-data-protection-regulation-gdpr-/
Flywheel
Status : Unknown
No Information found
​Kinsta
Status :​ They say they are fully GDPR compliant. But no details could be found.
​https://kinsta.com/wordpress-hosting-germany/
Update May 4th 2018
The Lowdown on GDPR Compliance for WordPress Users
A2 Hosting
Status : Currently working on it (Updated Mar 15, 2018)
See their latest news :
https://www.a2hosting.com/kb/does-a2-hosting-support/do-you-support-gdpr-compliance
​General Hosting Providers
​
Amazon AWS
Status : Ready. All AWS Services GDPR Ready (March 26th, 2018)
See their latest news :
https://aws.amazon.com/blogs/security/all-aws-services-gdpr-ready/