Don't know if this will work for everybody ... I'm on Mac 10.14.5 with Safari 12.1.1 and I tried the earlier advice about unsetting the "cross site tracking" option. That made Evernote work again in Safari.
BUT I was not happy at having to unset that option so I tried setting it again and VOILA! It still works. Must be some weird cookie that needs to be set and then is OK I guess.
Who knows what Safari 13 will do to me.