Add to wordpress.org/wordpress.org/public_html/wp-content/themes/pub/wporg-breathe/functions.php:
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add_action( 'init', 'untagged_RSS' );
function untagged_RSS(){
        add_feed( 'untagged', 'untagged_RSS_feed' );
}

function untagged_RSS_feed() {
        get_template_part( 'rss', 'untagged' );
}
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Create wordpress.org/wordpress.org/public_html/wp-content/themes/pub/wporg-breathe/rss-untagged.php
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<?php
/**
 * Template Name: Custom RSS Template - Untagged Posts
 */
$tags = get_terms('post_tag', array( 'fields'=>'ids' ) );
$args = array(
  'post_type' => 'post',`
  'tax_query' => array(
    array(
      'taxonomy' => 'post_tag',
      'field' => 'id',
      'terms' => $tags,
      'operator' => 'NOT IN'
    )
  )
);
$query = new WP_Query( $args );
header( 'Content-Type: '.feed_content_type( 'rss-http' ).'; charset='.get_option( 'blog_charset' ), true);
echo '<?xml version="1.0" encoding="'.get_option( 'blog_charset' ).'"?'.'>';
?>
<rss version="2.0"
        xmlns:content="http://purl.org/rss/1.0/modules/content/"
        xmlns:wfw="http://wellformedweb.org/CommentAPI/"
        xmlns:dc="http://purl.org/dc/elements/1.1/"
        xmlns:atom="http://www.w3.org/2005/Atom"
        xmlns:sy="http://purl.org/rss/1.0/modules/syndication/"
        xmlns:slash="http://purl.org/rss/1.0/modules/slash/"
        <?php do_action( 'rss2_ns' ); ?>>
<channel>
        <title><?php bloginfo_rss( 'name' ); ?> - Feed</title>
        <atom:link href="<?php self_link(); ?>" rel="self" type="application/rss+xml" />
        <link><?php bloginfo_rss( 'url' ) ?></link>
        <description><?php bloginfo_rss( 'description' ) ?></description>
        <lastBuildDate><?php echo mysql2date( 'D, d M Y H:i:s +0000', get_lastpostmodified( 'GMT' ), false); ?></lastBuildDate>
        <language><?php echo get_option( 'rss_language' ); ?></language>
        <sy:updatePeriod><?php echo apply_filters( 'rss_update_period', 'hourly' ); ?></sy:updatePeriod>
        <sy:updateFrequency><?php echo apply_filters( 'rss_update_frequency', '1' ); ?></sy:updateFrequency>
        <?php do_action( 'rss2_head' ); ?>
        <?php while($query->have_posts()) : $query->the_post(); ?>
                <item>
                        <title><?php the_title_rss(); ?></title>
                        <link><?php the_permalink_rss(); ?></link>
                        <pubDate><?php echo mysql2date( 'D, d M Y H:i:s +0000', get_post_time( 'Y-m-d H:i:s', true), false); ?></pubDate>
                        <dc:creator><?php the_author(); ?></dc:creator>
                        <guid isPermaLink="false"><?php the_guid(); ?></guid>
                        <description><![CDATA[<?php the_excerpt_rss() ?>]]></description>
                        <content:encoded><![CDATA[<?php the_excerpt_rss() ?>]]></content:encoded>
                        <?php rss_enclosure(); ?>
                        <?php do_action( 'rss2_item' ); ?>
                </item>
        <?php endwhile; ?>
</channel>
</rss>
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