function no_valid_user_no_rest($user) {
    if (!$user) {
        [add_filter](http://codex.wordpress.org/Function_Reference/add_filter)('rest_enabled', '__return_false');
        [add_filter](http://codex.wordpress.org/Function_Reference/add_filter)('rest_jsonp_enabled', '__return_false');
    }
    return $user;
}
[add_filter](http://codex.wordpress.org/Function_Reference/add_filter)('determine_current_user', 'no_valid_user_no_rest', 50);

Codex Entries