Exclude posts of specific categories from WordPress RSS feed. Source: http://www.jangro.com/excluding-posts-from-your-blog-feed/

exclude-categories-from-rss-feed.php

<?php

//*  Exclude posts of specific categories from RSS feed
function customprefix_exclude_categories_rss_feed($query) {
    if ($query->is_feed) {
        $query->set('cat', '-5, -11, -18'); // Precede category IDs with a minus sign
    }
    return $query;
}
add_filter('pre_get_posts', 'customprefix_exclude_categories_rss_feed');