If the character is set on this as a cultural trait, more power to them. (But yes, ew). I would work with the player to develop some guidelines. He is still nominally human (or whatever) and thus should have an inability to eat certain kinds of remains (undead, elementals, golems, etc.) There is also no way he could devour all of everything he kills. Who can eat a whole umber hulk between long rests?
I'd suggest that he has to eat a token of the creature he kills beyond that which is needed for sustenance. Never mind about poison glands, etc. If his people have this trait, they doubtless know how to prepare just about anything. It's a fantasy world, so don't worry about mundane things like parasites or transmissible diseases.
Ask him to limit actual consumption to organic beings. For something like a golem or an undead, he merely has to consume a token. Usually this can be done by burning the remains and inhaling the smoke or steam, or carving off a small bit (say, of a stone golem) and swallowing that. Anyone can pass a pebble.
If you want to reduce the squeakiness of cannibalism, you might require humanoid forms to be eaten while in Wild Shape.
If the player insists on complete devouring, that will probably require magic. He's a druid, give his circle a unique spell that lets them consume anything that they have killed. Make it quick, easy and magical. Then you don't have to wait around for several hours after every combat for the Otyugh stew to simmer properly. He'll have to dedicate a spell slot to the ability, but anyone who wants to play something so potentially disruptive or difficult to manage should be willing to pay something for the ability.