I've met pilots who have been asked to fly live animals... they didn't like doing it either because of the smell and noise, or because they suspected what was going to happen to the animals upon their arrival.
They voiced their opinions to the operator, but knew that they couldn't refuse to perform the flight on those grounds... so they did it grudgingly.
No real difference to flying munitions of war around the world, if you don't believe in that conflict. You do it because it's part of your job.
Breaking the law by flying certain cargoes is something different altogether.