Auto approve new users if their username is included in a predefined list

You might put this code in functions.php :

$GLOBALS['allowed_users']= ['mikejordan', 'jamesbrown', ...];


add_action('user_register','my_function');
function my_function($user_id){
    // get user data
    $user_info = get_userdata($user_id);
    if ( in_array($user_info->login, $GLOBALS['allowed_users'] ) )
    {
       $res = $wpdb->query($wpdb->prepare("SELECT activation_key from {$wpdb->signups} WHERE user_login = %s)", $user_info->login));
       if (!empty($res)) {
          wpmu_activate_signup( $res->activation_key );
       }

    }
}