If followed to the letter GDPR would've major repercussions on tax regulations because as a company you're legally bound to keep accounting records for at least 10 years whereas according to GDPR you're required to delete any record if asked by a person whose personal data appears in that record.
The solution in that case is that GDPR only applies if it doesn't contradict other, already existing laws.
So, where Blockchain applications facilitate legal requirements or don't manage personal data this should be perfectly fine but yes, other types of Blockchain applications are pretty much ruled out by GDPR.