Date fields can be programmatically added like this:
$entity->get($field_name)->offsetGet(0)->setValue(array($iso_date));
// or
$entity->get($field_name)->offsetGet(0)->setValue(array('value' =>$iso_date));But there is an exception when they are added like this:
$entity->get($field_name)->offsetGet(0)->get('value')->setValue($iso_date);This works for text fields, so I would expect it to work for all fields.