How on earth would I know what the cargo on board is intended for? Most of the time I don't even know what it is down there. If live animals are on board, would I know if the animals are going to a zoo, to be sold as pets, or to be released into the wilds of downtown Kansas City? I wouldn't know, nor would it be my place to ask.
I've carried unusual loads, ranging from weapons to equipment to animals to people (not much difference between the animals and the people) to cars, to things I can't talk about, to things I know nothing about. I've carried them into busy cities, rural areas, and combat zones. I'm not paid to decide who gets to fly or to determine what I can carry, save for making the determination of what is safe to carry.
Could I refuse to carry something? If it's unsafe, yes. If I don't like it? Sure, I could refuse...in lieu of submitting a letter of resignation.