I think I got it working although I didn’t quite get the result I expected based on the name “profile visibility”. I expected to see settings like “show my profile to group everyone/members/friends/logged in users”, “show me in the directory”, etc.
Instead the page that loaded shows the various Profile Fields and allows the use to toggle the visibility of each field. This seems very similar to the controls available when the user when editing their profile (where they can set these same visibility settings).
This file: …themes/ibuddy/buddypress/members/single/settings.php
was missing this
case 'profile' :
bp_get_template_part( 'members/single/settings/profile' );
break;