I found the root cause.
I disabled in my CKEditor the anchor plugin. If you take a look into the InputfieldCKEditor.module file you can see there is a check if the anchor plugin is disabled the HTML Purifier option "Attr.EnableID" is also disabled.
self::$purifier->set('Attr.EnableID', stripos($this->toolbar, 'anchor') !== false); // for anchor plugin use of id and name attributes
Is there a possibility to override that configuration, or must it be changed directly in the InputfieldCKEditor.module file?