Although we want to protect freedom of religion, it is not as fundamental as other rights. When two rights clash, we have to decide which should take precedence – for example, your freedom of action is limited by my right not to be punched in the face. Further, we will normally resolve clashes so as to first stop physical harm, followed by emotional or other harm. Freedom of religion, though important, comes further down the list.  In this case, the more “fundamental” of the rights in play is the right of the animal to be protected from unnecessary pain. It is more closely linked to reducing suffering, which an appropriate goal for society. So in this particular case, we should put the animals first.