Your feeds still reach RSS readers, and Google is told plainly that they aren't pages to index.
What it does
It's a must use plugin just a few lines long: a plugin WordPress always loads, without activation, from the wp-content/mu-plugins folder. Every time a feed is served, whether it's the posts feed or the feed for a category, a tag or the comments, it adds the X-Robots-Tag: noindex, noarchive header.
It doesn't block anything: the feed is still available to RSS readers and any service that uses it. It only asks search engines not to offer it as a result or keep a cached copy.

/wp-content/mu-plugins.Why feeds
WordPress generates a feed for almost everything: the blog, each category, each tag, the comments. They're XML for RSS readers, not pages for search, but Google crawls them anyway and usually ends up leaving them out of the index on its own, as Crawled - currently not indexed in Search Console. With the header, you ask for it explicitly instead of leaving it to Google's judgement.
How it works
- Copy the file into
wp-content/mu-plugins(create the folder if it doesn't exist). - WordPress loads it automatically: it shows up under Plugins, on the Must-Use tab, with no activate button.
- Open
/feed/on your site and check the response headers for X-Robots-Tag: noindex, noarchive.
Requirements
- Installed as a must use plugin in
wp-content/mu-plugins.
Want it on your WordPress site?
We'll install it and check that your feeds keep working for whoever uses them.