Filter authors on meta value

Is there a specific reason you aren’t using WP_User_Query? It would make it easier to do what you want to. You can read up on it here.

Something along these lines would solve your problem, as far as I understand it:

$args = array(
   "meta_key" => "ArtistCategory",
   "meta_value" => "X" //or "Z"
);
$authors = new WP_User_Query($args);
if (!empty($authors)) {
   echo '<ul>';
   foreach ($authors as $author){
       //However you want to echo each author.
   }
   echo '</ul>';
} 
else {
   echo 'No authors found';
}