How to add a body class based on a custom taxonomy term

What is the job of $section_name? Also you must get an return; you if statement kill the default return. It is important, if your if statement fails.

maybe this works, but not tested, write from scratch.

add_filter( 'body_class', 'section_id_class' );
// add classes to body based on custom taxonomy ('sections')
// examples: section-about-us, section-start, section-nyc
function section_id_class( $classes ) {
    global $post;

    $section_terms = get_the_terms( $post->ID, 'section' );
    if ( $section_terms && ! is_wp_error( $section_terms ) ) {
        foreach ($section_terms as $term) {
            $classes[] = 'section-' . $term->slug;
        }
    }

    return $classes;
}