Chiming in to say I'm experiencing the same issue on iOS 13. Evernote consistently crashes on the splash screen. And as you mentioned, Evernote worked just fine until updating it to the most recent version.
I also tried it after updating to beta 2 of iOS 13 and it still crashes.
(Of course, can't really blame Evernote when we're on beta software but kind of strange since it worked just fine on the previous version)
EDIT: Update! I deleted the app, restarted my phone, and re-installed. So far no more crashes!