Hi Dianne,
Thank you for your patience.

Please remove the old code and use the following.

/**
 * Returns a list of user links sorted alphabetically.
 *
 * @param array $group_users user ids.
 *
 * @return string
 */
function bp_custom_get_alpha_sorted_user_links( $group_users ) {

	if ( empty( $group_users ) ) {
		return '';
	}

	$group_user_ids = wp_list_pluck( $group_users, 'user_id' );

	$users = get_users(
		array(
			'include' => $group_user_ids,
			'orderby' => 'display_name',
			'order'   => 'ASC',
		)
	);

	$markup = '';

	foreach ( $users as $user ) {
		$markup .= sprintf( '<a href="%1$s" class="custom-user-group-user-link">%2$s</a>', esc_url( bp_core_get_user_domain( $user->ID ) ), bp_core_get_user_displayname( $user->ID ) );
	}

	return $markup;
}

function user_world_memberships( $atts, $content = '' ) {

	$atts = shortcode_atts(
		array(
			'user_id'            => bp_displayed_user_id(),
			'type'               => 'alphabetical',
			'order'              => 'ASC',
			'page'               => 1,
			'per_page'           => - 1,
			'group_type'         => '',
			'group_type__in'     => '',
			'group_type__not_in' => '',
			'group_role'         => '', // 'admin' , 'mod', 'member'.
			'list_admins'        => 0,
		),
		$atts,
		'member_worlds'
	);

	$list_admins = (bool) $atts['list_admins'];
	$user_groups = array();

	if ( 'admin' === $atts['group_role'] ) {
		$user_groups = bp_get_user_groups(
			$atts['user_id'],
			array(
				'is_admin' => true,
				'per_page' => $atts['per_page'],
				'page'     => $atts['page'],
			)
		);
	} elseif ( 'mod' === $atts['group_role'] ) {
		$user_groups = bp_get_user_groups(
			$atts['user_id'],
			array(
				'is_mod'   => true,
				'per_page' => $atts['per_page'],
				'page'     => $atts['page'],
			)
		);
	}

	if ( in_array( $atts['group_role'], array( 'admin', 'mod' ), true ) ) {
		if ( empty( $user_groups ) ) {
			return '';
		}

		$group_ids       = array_keys( $user_groups );
		$atts['include'] = $group_ids;
		unset( $atts['user_id'] );
	}

	$groups = groups_get_groups( $atts );

	$groups = $groups['groups'];
	if ( empty( $groups ) ) {
		return '';
	}

	$list = '';
	foreach ( $groups as $group ) {
		$admin_markup = '';
		if ( $list_admins ) {
			$admin_markup = bp_custom_get_alpha_sorted_user_links( groups_get_group_admins( $group->id ) );
		}
		$list .= sprintf( '<li><a title="View %1$s" href="%2$s" class="custom-user-group-group-link">%3$s</a>%4$s</li>', esc_attr( $group->name ), esc_url( bp_get_group_permalink( $group ) ), esc_html( $group->name ), $admin_markup );
	}

	if ( ! empty( $list ) ) {
		$list = "<ul class='custom-user-group-list'>{$list}</ul>";
	}

	return $list;
}

add_shortcode('member_worlds', 'user_world_memberships');

You can pass group_role and list_admins options to list specific groups as in your initial requirement. It should handle most of the earlier use case.

Regards
Brajesh