4 foot fence, took the turkey outside it.
Coyote, dog, fox, cougar, bobcat, racoon (less likely). All are capable of carrying a turkey over a 4 foot fence. The coon is borderline. That's a lot of dead animal for a coon to carry over a fence.
If you look at the fence, you may gleen some additional information. If there are obvious signs of the carcass being dragged up and over the fence, you can be pretty sure the predator climbed the fence. If there are no signs on the fence, it may have simply leaped the fence carrying the carcass.
Breast and guts were consumed.
That's fairly typical of any predator. Humans are about the only thing interested in "meat". It's the guts that are prime for predators typically. This would pretty well knock out domestic dog. They will tend to play with the dead bird, and sloppily gnaw all over it.
Being consumed effectively on site reduces the likelyhood of it being coyote or dog. They tend to carry prey off to a location they perceive as safe. I'm not familiar with cats enough to comment on their habits.