If the article is correct, and it's impossible to make blockchain GDPR-compliant without turning it into a simple lookup table, then the number of potential blockchain applications in the EU has just gone to absolute zero, along with the number of potential blockchain applications that involve the EU in any way whatsoever.
That would be delicious, if a technology designed by privacy advocates was laid low by privacy concerns.
I know this is a late post, but I just wanted to add...
The article that was linked to was mainly relevant only to permissioned blockchains. You can be sure that anyone who is actually serious about privacy is not going to use a permissioned blockchain. An open blockchain that is privacy focused is not going to store any PII data on it anyway and therefore the entire article and GDPR is not applicable in that case.
While the article does make some good points in regards to permissioned blockchains, I think if anything, it misses the real point about how permissioned blockchains often don't provide any more benefit above and beyond what relational databases already provide organizations. There is so much blockchain hype out there looking to find ways to implement blockchain tech without actually looking at the problem that needs solving and what tech is best suited for solving it. Relational databases are also append databases like blockchains in the way that their logging takes place, they're just missing the cryptography components that blockchains utilize. You can still distribute relational databases in much the same way as you could a blockchain. If a blockchain is centrally controlled, managed, and permissioned to the point where being a trustless system is not a feature, then cryptography won't provide much of a benefit above what a typical relational database already provides.
In this regard, blockchains are very inefficient databases to run when compared to relational databases. In a permissioned blockchain where you don't care about being trustless, you can centrally enforce consensus on the network. In that case, proof of work is then not necessary to prevent double-spending. If that's the case, then there isn't much of a benefit of running a blockchain. Why create an immutable and decentralized ledger that is in the hands of a centralized entity that can decide whether or not immutability is actually true or not at any point in time?
This is why tokenized blockchain applications are all mostly hype at this point. It makes much more sense to develop those centrally managed 2nd layer blockchain applications onto an existing trustless decentralized base-layer blockchain like Bitcoin. This way you're backed by true immutability of the most secure blockchain on the planet, but any type of data you want to put into your application to make it work can be applied off-chain in ways that will work with regulations instead of against them. But don't tell this to any ICO developers/investors...