Presumably an app focused on privacy wouldn't even _have_ an account for the user to sign up with? Just let them install the app and off they go.
You could maybe offer a cloud save feature (for users who want that) like Duck Duck Go does for settings.
When the user wants to save something they enter some phrase/password/whatever with which they can later retrieve it.
This would allow users to change devices or reinstall without loosing their data temporarily. Maybe delete it after it’s been retrieved?