BuddyPress.org

Ok, here is a css solution.

#wp-admin-bar ul li#bp-adminbar-authors-menu{display:none;}

It will remove that for 100% sure if you put it at the bottom of the child theme css.

but I still believe that drop down has something to do with some other plugin, as your bp-core-adminbar.php says it as “Blog Author” while the list says “Shop Owners”