wp_list_categories() – current-cat class also inside posts?

Yes off course. You just need to get the term id and put it on the args. Check wp_list_categories()

function wr_list_taxonomy($taxonomy, $orderby, $hierarchical, $cat_id) {
    $show_count   = 0;
    $pad_counts   = 0;
    $title="";
    $cat_id = 0;

    $args = array(
      'taxonomy'     => $taxonomy,
      'orderby'      => $orderby,
      'show_count'   => $show_count,
      'pad_counts'   => $pad_counts,
      'hierarchical' => $hierarchical,
      'title_li'     => $title,
      'current_category' => $cat_id
    );

    return wp_list_categories( $args );
}

You have to pass the category id or term id. To make it work.

How Do You Get Category ID?

For Example:

    global $post;
    $taxonomy = 'my-tax';
    $term_id = 0;
    if(is_singular('post')){ // post type is optional.
      $terms = wp_get_post_terms( $post->ID, $taxonomy, array("fields" => "ids") );
      if(!empty($terms))
        $term_id = $terms[0]; //we need only one term id
    }

   wr_list_taxonomy($taxonomy, $orderby, $hierarchical, $term_id);

Its just a simple example and there are other ways to do it. It depends on where you are using the code.