Temporary quick solution is to exclude debug-toolbar scripts from script map
For example if you exclude jquery.js from script map. You may also exclude these scripgs

this code is in Controller::init

$cs = Yii::app()->clientScript;
$cs->scriptMap["jquery.js"] = false;

$cs->scriptMap['yii.debugtoolbar.js'] = false;
$cs->scriptMap['yii.debugtoolbar.css'] = false;

but there is another problem that toolbar generate service info that contains in layout
I solve this problem (in my case it is at module, but you also can do it at the same Controller::init) by disabling debug toolbar

/* @var CLogRouter $log */
$log = Yii::app()->log;
foreach($log->routes as $logRoute) {
if($logRoute instanceof YiiDebugToolbarRoute) {
$logRoute->enabled = false;
}
}