Due to the nature of the default robots.txt and the meta tags in Lemmy, search engines will index even non-local communities. This leads to results that are undesirable, such as unrelated/undesirable content being associated with your instance.

As of today, lemmy-ui does not allow hiding non-local (or any) communities from Google and other search engines. If you, like me, do not want your instance to be associated with other content, you can add a custom robots.txt and response headers to avoid indexing.

In nginx, simply add this:

# Disallow all search engines
location / {
  ...
  add_header X-Robots-Tag noindex;
}

location = /robots.txt {
    add_header Content-Type text/plain;
    return 200 "User-agent: *\nDisallow: /\n";
}

Here's a commit in my fork of the lemmy-ansible playbook. And here's a corresponding issue I opened in lemmy-ui.

I hope this helps someone :-)