The "livestock" word is very vague. Typically chickens are not livestock, but rather they are poultry or fowl. Livestock most commonly refers to cows, sheep, horses, goats, pigs. Where I live all these animals are listed out so it is very clear. And poultry (chickens, ducks, geese, turkeys) have their own category and their own ordinance.
I'm with you, I'm not sure I would pursue it or ignore it. When I was a kid we had chickens in our subdivision and it never occurred to us to see if it was all right. I am wondering what your town says regarding rabbits? Livestock? Or rodent?
I hope it works out for you. If these small towns were smart they would simply collect a "zoning fee" and make a little cash on the side every year per animal.
Good luck,
Jenny