Here is one way to think of this. Any EU citizen has a "right to be forgotten". If there is nothing in your records to identify that person, the you don't need to provide that ability.
let's say I'm a shop and i allow btc payments, but I include the customers info in the transaction or something to such an effect. then I'm in violation, and must pay a fine (since I can never delete that info). The network has nothing to do with this, and nobody else on the network is party to the violation.
Now we have a way to estimate the cost and we can just put that on top of the cost of using the service.
Boom, privacy bought.
You don't realise how absurd GDPR is?
There are also blockchain style social networks such as steem that create things that are like reddit: https://steem.io / https://steemit.com . Again, freeform public text blobs that can have private info.
If you create any censorship resistant publishing software, lets say to report on human rights violations in some sort of dictatorship, you also create something that can be used to violate the GDPR.
https://en.wikipedia.org/wiki/General_Data_Protection_Regula...