We as a species use animal bodies for so many different purposes that it's hard to keep track sometimes. Most self-proclaimed vegans have probably slipped up without even realizing it, ingesting bone-derived gelatin or using animal glue on accident. It's hard to avoid it when it's so invisibly prevalent in so many things. Obviously, avoiding meat and dairy is the easiest way to stop supporting factory livestock farms, but strict vegans might be interested to know what other innocuous foods and products are made with parts of animals. Here's a list of a few things that are unexpectedly not vegan-safe.
Sugar
The cane plant may be just that--a plant--but its white, crystalized juices are quite literally bone-bleached. Or used to be, at least, though there's no good way of telling whether a given sugar company still uses animal-derived purifiers to whiten their sugar. In order to get that bright white, you used to have to run your sweetener through charcoal filters made from burning the bones of livestock. Not exactly the sweetest procedure. It's best to get raw, natural cane sugar or agave nectar to ensure you're eating bone-free.
Beer
Water, yeast, malt, hops--all these sound pretty vegan-friendly, but some beer production techniques use more animal products than you might think. Stouts and other darker beers sometimes use milk sugar to augment their flavor. Keep an eye out for milk stouts--they mean it literally. But even your everyday can of PBR is likely made with animal parts. Breweries use isinglass, a substance derived from the swim bladders of fish, to clarify their beers before they make it into the can or bottle.
Apple juice
Even fruit juices, which seem naturally vegan enough, can be clarified with gelatin in a manner similar to the way beers are clarified with isinglass. Natural ciders or cloudier juices might not have gone through the clarification process.
Some jams
While all natural fruit preserves are probably vegan-safe, mass-produced jams sometimes throw in a little gelatin for texture. Stay away from the Smuckers if you want to avoid bone-goo.
Paintballs
To be fair, I don't know any vegan paintballers. Maybe they're aware that the casing on the game's ammunition is typically made out of gelatin.
Harps
I don't know any vegan harpists out there, either, but I had no idea that harp strings were made from animals. Animal intestines may be the last thing on my mind when I see a harpist at the symphony or another classy venue, but most high quality harps do indeed use strings made of catgut. Catgut itself is rather a misnomer--it refers to the innards of sheep or goats, not felines, but it's still very much not vegan.
Tattoos
Now, I do know quite a few tattooed vegans, and I'm not sure all of them did their homework. There are definitely plant-based skin dyes out there, but most black ink in tattoos is made from bone black--i.e. that charcoal made from burning animal bones. You typically have to ask around to find tattoo artists that use exclusively vegan inks. The more you know!
