I think it is technically already illegal for EU citizens's data to exist on non-EU blockchains, so a legal cryptocurrency could only exist within the EU or any country with a data-sharing agreement (which I do not think currently includes the US right now).
So just listing things they could do:
Make it illegal to host the data/be a validator would relegate crypto to something that is only used for illegal purposes.
Write into law that GDPR still applies to blockchains, the validators cannot stay anonymous so they either remove the data from the blockchain or get police knocking on their door.
Any other use that this would be illegal so could never be used for anything legal inside the EU, lowering it down to a similar priority as piracy, being effectively neutralized, aka not affecting the majority of EU citizen.