To customize the style of single product page for some particular category of products on WooCommerce you can use the following code in your functions.php file.

function woo_custom_taxonomy_in_body_class($classes){
  if( is_singular('product')) {
    $custom_terms = get_the_terms(0, 'product_cat');
    if ($custom_terms) {
      foreach ($custom_terms as $custom_term) {
        $classes[] = 'product_cat_' . $custom_term->slug;
      }
    }
  }
  return $classes;
}
 
add_filter( 'body_class', 'woo_custom_taxonomy_in_body_class' );

If you want to add the tags just replace product_cat with product_tag