The text for parasite is on the Monster Organ basic resource card and only applies to that card.
You would never choose to eat it.
There is a disorder that makes you eat things involuntarily. If you ate the Monster organ because of this you would suffer the additional penalties of the parasite written on the Monster Organ card.
Does a binge eater only eat resources given specifically to them directly (gain a basic resource when survivor takes an action, etc)? Or would that also happen if the party receives items during the aftermath that include consumables? We've played it as the former, but I've been too lazy to look up the latter possibility.