Solution found : to make a case-sensitive search for a meta_key / meta_value pair : a hardcoded mysql query on the usermeta table with the BINARY keyword, with get_results() method of $wpdb object:
global $wpdb;
$sql = $wpdb->prepare( "SELECT user_id FROM {$wpdb->prefix}usermeta
WHERE meta_key = 'unique_id'
AND BINARY meta_value="unique_id_value"");
$wordpress_user_query = $wpdb->get_results( $sql);