add_action( 'template_redirect', 'rw_relative_urls' );

function rw_relative_urls() {
    if ( is_feed() )
        return;

    $filters = array(
        'post_link',       // Normal post link
        'post_type_link',  // Custom post type link
        'page_link',       // Page link
        'attachment_link', // Attachment link
        'get_shortlink',   // Shortlink
        'post_type_archive_link',    // Post type archive link
        'get_pagenum_link',          // Paginated link
        'get_comments_pagenum_link', // Paginated comment link
        'term_link',   // Term link, including category, tag
        'search_link', // Search link
        'day_link',   // Date archive link
        'month_link',
        'year_link',
    );
    foreach ( $filters as $filter ) {
        add_filter( $filter, 'wp_make_link_relative' );
    }
}