I think I found a bug on the marketpress plugin:
On marketpress line #1629:
if (empty($_POST['zip']) && $_POST['country'] != 'IE') //no postal code in Ireland $this->cart_checkout_error(__('Please enter your Zip/Postal Code.', 'mp'), 'zip');
Therefore it is allowed to leave zip code for Ireland.
Same file, on line #2202:
//check required fields if ( empty($address1) || empty($city) || empty($zip) || empty($country) || !(is_array($cart) && count($cart)) ) return false;
Therefore if a shipment to Ireland has not postcode no shipping is charged.