mrepic

A partir do Woocommerce 3.0 você pode fazer isso usando priority.
Experimenta mudar o código para:

add_filter("woocommerce_checkout_fields", "order_fields");

function order_fields($fields) {

    $order = array(
        "billing_first_name", 
        "billing_last_name", 
	"billing_email", 
        "billing_phone",
	"billing_postcode", 
	"billing_address_2", 
        "billing_address_1", 
        "billing_neighborhood", 
        "billing_city", 
        "billing_state", 
        "billing_country" 
    );
    $i = 10;
    foreach($order as $field)
    {
        $fields["billing"][$field]["priority"] = $i;
        $i++;
    }
    return $fields;
}