Hello Keith,
Please understand that we always abide the standards of WordPress. By default, password protection is only applied to the post/page content in WordPress. This is why the sidebar is still visible even if you added password for the content. It is evident in this article: https://codex.wordpress.org/Using_Password_Protection
Having to remove the sidebars as well, will be done with customizations already. Just do not be disappointed just yet. Anyways, to resolve your issue, will just us the article as a reference. Since you have your child theme active and ready, please follow the following steps below:
1] Using Notepad or TextEdit or Sublime Text or any text editor, please create a new file in your local machine.
2] Insert the following code into that new file
<?php
// =============================================================================
// VIEWS/ETHOS/WP-SIDEBAR.PHP
// -----------------------------------------------------------------------------
// Sidebar output for Ethos.
// =============================================================================
?>
<?php if ( x_get_content_layout() != 'full-width' ) : ?>
<aside class="<?php x_sidebar_class(); ?>" role="complementary">
<?php if ( !post_password_required() ) ?>
<?php if ( get_option( 'ups_sidebars' ) != array() ) : ?>
<?php dynamic_sidebar( apply_filters( 'ups_sidebar', 'sidebar-main' ) ); ?>
<?php else : ?>
<?php dynamic_sidebar( 'sidebar-main' ); ?>
<?php endif; ?>
<?php endif; ?>
</aside>
<?php endif; ?>
3] Save the file named as wp-sidebar.php
4] Upload this file to your server in the child theme’s folder wp-content/themes/x-child/framework/views/ethos/ or wp-content/themes/pro-child/framework/views/ethos/ if you are using Pro theme.
Just make sure to create the folder path since it does not exist in your child theme yet.
Please let us know how it goes.