> Let say I use some service, then I violate policies of that company, then I exercise my "right to forget", and after they delete my data I sign up again and repeat the entire thing?
In this case a business (or 'data controller' in GDPR lingo) can use 'legitimate interest' as a lawful basis for processing the users information. Of course the data you kept would have to be proportional to what you're doing. For example, it would be hard to argue that you needed to keep the users billing address history if your services used a simple email black list (this is the 'data minimisation' principle).
> how does that work in regards to book keeping and tax policies, where you are required to have data about your clients?
As a rule of thumb, if you're using some personal data to comply with another piece of law then that usage is generally exempt from GDPR.
Source: https://ico.org.uk/for-organisations/guide-to-data-protectio...
Then that would be a legitimate interest, and you could store that information for a period of time that is reasonable for processing refund requests.
But you would be barred from using that same information for a different purpose, e.g. the loyalty program.
GDPR article 25 requires systems to be have privacy built in, so a system such as the one you describe where a separation of these concerns is impossible, would probably itself be in violation of the regulation.
1. Nothing user has is truly hash-able, (email can be replaced, there are people with the same name/dob/place of birth, address is not permanent attribute...)
2. Hash key can have duplicates - so those collisions would block different users (probably not for small companies but for FB with 2 billion users something worth considering.)