Of course I'm missing all kinds of key context, but going off of your description I'd seriously consider letting him leave. Come up with some sort of deal that you're both satisfied by - money, a loan, converting his shares into non voting shares, whatever, but let him go.

I say this as the technical co-founder of an EU based messaging startup with the vast majority of users and customers being subject to the GDPR. If your co-founder finds a little bit of legislation to be so troublesome that he wants to quit, then he's going to be worthless when things actually get difficult. Even if the worst case is true, in legal terms, and you decide that you're forced to redesign the system to make the right to be forgotten (and while I'm not a lawyer I really doubt that that is a sane explanation of the GDPR), then it's just some refactoring work. It's not fundamental to the design or business model of your app (you're a messaging app, not a "sell user data app") - it's just an efficiency thing. If your co-founder can't even deal with that, then I worry that he defibitely can't deal with the emotional rollercoaster that will start when you actually launch.

That said, and IANAL, but I really wouldn't sweat it. If you can run a custom query to delete user data when requested then you're all good. Use that to see how many right-to-be-forgotten requests you actually get and consider automating things only after you know that it's going to pay off.