The GDPR itself doesn’t use the term organisation, it refers to data controllers and data processors.
A “data controller” refers to a person, company, or other body which decides the purposes and methods of processing personal data.
A “data processor” refers to a person, company, or other body which processes personal data on behalf of a data controller.
As someone from within the EU working in data the fediverse is absolutely not a long way off having to consider this, GDPR impacts even the smallest businesses or voluntary groups - it’s just how we handle data.
To make it easier to grasp GDPR is about your rights over your data, those don’t change depending on who is processing it, nor does the processors obligation, however what would be considered appropriate safeguards would scale with the size and intent of your organisation - it would be silly for my local shop to have a data protection officer.
I suppose the question would become who is the controller, is it the person who provides the software or the person who provides the servers? Typically it’s the servers.
New response just dropped