Make RSS feed only accesible by Mailchimp

Finally, the solution has been, as birgire pointed out, creating a custom feed and only allowing access to that URL:

// Create new feed
add_action('init', 'customRSS');
function customRSS(){
    add_feed('supersecretfeed', 'customRSSFunc');
}

function customRSSFunc(){
    get_template_part('rss', 'supersecretfeed');
}

Then, as the site is private, I had to allow public access to that specific URL, adding the is_feed option:

// Ban non logged users
function protect_whole_site() {
    if(! is_page( 'wp-login.php' ) && ! is_feed('supersecretfeed') && ! is_user_logged_in() ) {
        auth_redirect(); 
    }
}