Hide product categories and taxonomy terms in menu if empty

Not sure about the custom taxonomy, however I have used this code before to remove empty categories. You can add it to functions.php.

add_filter( 'wp_get_nav_menu_items', 'nav_remove_empty_category_menu_item', 10, 3 );
function nav_remove_empty_category_menu_item ( $items, $menu, $args ) {
    global $wpdb;
    $nopost = $wpdb->get_col( "SELECT term_taxonomy_id FROM $wpdb->term_taxonomy WHERE count = 0" );
    foreach ( $items as $key => $item ) {
        if ( ( 'taxonomy' == $item->type ) && ( in_array( $item->object_id, $nopost ) ) ) {
            unset( $items[$key] );
        }
    }
    return $items;
}