If you go to the "share" button, you can send a link of your map to any non-Remix user (guest). That guest can see the map, but will have a "read-only" version. They will be able to move around or select different lines, But their work will not overwrite your original map.
Guest viewers will be able to "add a comment" using the comment box at the top left. Comments will then be sent to the email address of the map owner.