Is it permissible to consume food products that contain the additive E471, knowing that its origin is unknown and could be animal-derived (including pork), and it is difficult to avoid, and is it obligatory to investigate or to avoid it altogether?

Doubt concerning an unknown additive being of animal origin or pork is not to be entertained, for the default assumption in Muslim lands is that food is free from pork. This default assumption is not to be abandoned except with certainty or a strong presumption. Food is not to be discarded based on doubt, and the basic principle regarding foodstuffs is permissibility until proof of prohibition is established.