Have been working a lot with the WP-Rest API lately, and getting it to display certain content on the public side. I needed a way to show the taxonomy terms so we can dynamically populate a front-end filtering interface on another site using the “server” site as the backend.

class all_terms
{
    public function __construct()
    {
        $version = '2';
        $namespace = 'wp/v' . $version;
        $base = 'all-terms';
        register_rest_route($namespace, '/' . $base, array(
            'methods' => 'GET',
            'callback' => array($this, 'get_all_terms'),
        ));
    }

    public function get_all_terms($object)
    {
        $return = array();

        // Get taxonomies
        $args = array(
            'public' => true,
            '_builtin' => false
        );
        $output = 'names'; // or objects
        $operator = 'and'; // 'and' or 'or'
        $taxonomies = get_taxonomies($args, $output, $operator);
        foreach ($taxonomies as $key => $taxonomy_name) {
            if($taxonomy_name = $_GET['term']){
            $return = get_terms($taxonomy_name);
        }
        }
        return new WP_REST_Response($return, 200);
    }
}