Add noindex to your WordPress website using the X-Robots-Tag header

add_noindex_for_feeds.php

<?php
// add this code to your theme's functions.php file

function add_noindex_for_feeds($headers) {
	$req_uri = filter_input(INPUT_SERVER, 'REQUEST_URI');
	if ( '/feed/' == substr($req_uri, -6) ) {
		$headers['X-Robots-Tag'] = 'noindex';
	}
    return $headers;
}
add_filter('wp_headers', 'add_noindex_for_feeds');

Strange, the is_feed() conditional tag isn't working here...

Anyway I'm using this function now because the Google bot ignores these robots.txt rule on many sites I manage:

User-agent: *
Disallow: */feed/