Banks Torn on GDPR Day as EU Pulls Them in Opposite Directions

European banks are agonizing over how to handle the mountains of client data at their disposal -- and not just because Facebook Inc.’s privacy scandal showed them the potential pitfalls of getting it wrong.

Sweeping new European Union rules kicked in May 25, setting out strict new boundaries on the information companies can gather about their clients and how they use it. Violators can be fined as much as 4 percent of their global revenues.

But for banks, that’s just the beginning. Lenders must also prepare for separate rules -- in a law known as PSD2 -- requiring them to ...