in user/profile/lib.php

function profile_definition(&$mform) {

the Header is always printed, even if all the custom fields are set to "not visible"

this line:
if ($fields = get_records_select('user_info_field', "categoryid=$category->id", 'sortorder ASC')) {

should be something like:
if ($fields = get_records_select('user_info_field', "categoryid=$category->id and visible<>0", 'sortorder ASC')) {