I had the problem that I would log into the Evernote Webclipper, it would ask me to sign in. Then it would bring up a box that it uses cookies, but never let me clip anything. I checked that I have cookies allowed for Evernote. Still only this dialog box came up, without actually clipping anything. (Webclipper 6.13.2, Safari 12.1.2, macOS 10.14.6)
I went to the webclipper page on the Evernote website. https://evernote.com/features/webclipper
Clicked that I would like to "Get Webclipper". It took me to the Mac APP store to download. I installed from the app store. App Name: Evernote Web Clipper
After installation, the Safari Preferences > Extensions - Box Came up. I deselected the old webclipper 6.13.2. And I selected the new webclipper extenstion 7.12.3
It works now. I suppose I could uninstall the old webclipper now.
Hope this helps.