BuddyPress requires ‘manage_options’ capability in order a user has access to the “Groups” and “Activity” menu items. So we have to grant to a role at least the ‘read’ and ‘manage_options’ user capabilities to allow it the access to the “Groups” at wp-admin.

It’s possible to block “Settings” and other admin menu items protected by the same ‘manage_options” capability, using User Role Editor Pro add-on “Admin Menu Access