Are chicken gizzards celiac safe? Wheat is frequently included in chicken feed. Partially-digested wheat, therefore, would likely be present in chickens' gizzards before butchering.

However, the chicken gizzards seen for sale in grocery stores don't appear to have any leftover feed residue in them -- apparently, any macroscopic amounts of undigested feed remaining in the gizzard are (somehow) removed during processing.

Do the human-edible parts of the gizzard come in direct contact with the bird's digestive contents? If so, would a person with celiac disease need to worry about potentially ingesting residual gluten from the chicken's feed when eating gizzards?
Chicken gizzards have a tough membrane on the inside (the only part that gets in contact with the bird's food) that holds the stones + grit + food during the grinding part of the digestion process.

That membrane is always removed before selling the gizzards, so I don't believe there will be any residue there - I never saw one sold with that membrane.