ICANN don't register domains, the registrars contract with ICANN to offer that service to their customers.
The GDPR will invalidate part of the contract between the registrars and ICANN insofar as it involves doing business in the EU - you can't be bound by a contract to break the law - but the rest of the registrars' contracts with their individual custmoers will remain in force.
If the registrars fail to abide by the GDPR they will be prosecuted by the appropriate authority in the relevant EU country. If they withdraw their services they will be subject to claims for breach of contract by their customers and lose a significant part of their revenue.
With luck, it will be ICANN that explodes, but the more useless and idle an organisation is, the longer it seems to persist in its irrelevance.
Biting the hand that feeds IT
