Add support for hook_entity_view_mode_alter().

And here's a patch so you have the entity that contains the field collection. Useful if you need to change the view mode based on settings of that entity.

Don't use this patch. See comment 2.

I just found out that you can get the host entity from the field collection entity by using hostEntity().

function MYMODULE_entity_view_mode_alter(&$view_mode, $context) {
  $host_entity = $context['entity']->hostEntity();
}

This means the second patch provides redundant functionality. The major difference being an explicit definition of the host entity instead of relying on someone to be aware that it's accessible via the existing entity wrapper. Just a heads up to anyone who is planning on using on of the patches. The first is enough.