Index: class-wp-customize-manager.php
===================================================================
--- class-wp-customize-manager.php	(revision 48938)
+++ class-wp-customize-manager.php	(working copy)
@@ -492,8 +492,21 @@
 
 		return '_default_wp_die_handler';
 	}
-
 	/**
+	 * Redirects a URL to the 404 page if changeset UUID does not exists for unauthenticated users
+	 *
+	 * @since 5.6.0
+	 *
+	 * @param bool     $bypass Pass-through of the pre_handle_404 filter value.
+	 * @param WP_Query $query  The WP_Query object.
+	 * @return bool Bypass value.
+	 */
+	public function customize_changeset_preview_redirect( $bypass, $query ) {
+		$query->set_404();
+		status_header(404);
+		return $bypass;
+	}
+	/**
 	 * Start preview and customize theme.
 	 *
 	 * Check if customize query variable exist. Init filters to filter the current theme.
@@ -547,10 +560,17 @@
 		 * In this way, the UUID serves as a secret key. If the messenger channel is present,
 		 * then send unauthenticated code to prompt re-auth.
 		 */
-		if ( ! current_user_can( 'customize' ) && ! $this->changeset_post_id() ) {
-			$this->wp_die( $this->messenger_channel ? 0 : -1, __( 'Non-existent changeset UUID.' ) );
-		}
-
+		if (! current_user_can( 'customize' ) && ! $this->changeset_post_id() ) {
+		    add_filter( 'pre_handle_404', array( $this, 'customize_changeset_preview_redirect' ), 1, 2 );
+	}
 		if ( ! headers_sent() ) {
 			send_origin_headers();
 		}