I also don't like the AMLR at all, but it has to be clarified that some privacy coin services are only banned for crypto service providers. The wording also doesn't prohibit privacy coins accounts per se, but it prohibits to offer accounts based on privacy coin technology which allow you to hide identities and transactions. This is a subtle difference, but there may be allowed to offer accounts for XMR and friends if the client for example can prove the origin of the funds. Many of these EU regulations are based on FATF guidelines.

I would however not mix this with the discussion about the GDPR and data protection. There is a better article about the problem on Forbes.

The funny thing about that is that the EU is proposing anonymization techniques which conflict with the AMLR approach. So if things go completely wrong, it would be legal in the EU only to run full nodes of privacy coins like Monero because they respect the GDPR, but you couldn't sell the coins transferred on these chains on centralized exchanges operating in the EU area but only via P2P...

I wonder if stealth addresses would solve that problem; probably they would if they were as "stealthy" as on Monero, but I think the "Bitcoin stealth addresses" in the vein of BIP 47 payment codes may not be enough.