Probably not. I really have mixed emotions about GDPR being a SaaS founder. It seems overstepping and heavy handed that the EU can enact laws that affect American's and American companies. The EU can do what it wants, but generally I am against regulation as it promotes bureaucracy, stifles innovation, and creates fluff and burden's especially on small companies such Chief Data Protection Officer and Chief Data Offic…
This bothers me a lot as well. The EU shouldn't have domain over American companies. There's a reason that there isn't a ton of Tech companies in places like Germany.
Just don't accept European customer's data and you're fine.