How can I share an album publicly (i.e. with non-icloud users) on iCloud
Share it with the person - then once the album is created, in Photos, there will be an icon with a head in a circle. This is the settings pane for the shared photo album.

Full Procedure:


Create Shared iCloud Album
Select new Shared Album from left side pane in Photos
Click head in a circle icon to get an option to turn on the Public Website.
Check that box and it gives you the URL.


Sample:



Not obvious, but it works.