I'm having this issue too.
I can log in absolutely fine from the app on my macbook, my iPhone, from the web version on a PC... but it won't let me log in via the app on my older 2012 iPad (4th gen). I supposedly downloaded the version of evernote that was compatible for my system (iOS 10.3.3) as prompted by the Appstore, but every time I enter my credentials I get the "error sign in" message as stated above...
I'd like to add that I tried uninstalling and installing again... also uninstalling, re-booting device, then installing again. Nothing works so far.