In some religions, animal sacrifices are an integral part of many religious rituals. Sacrifices of various sorts -- plant, animal, and even human -- have been integral to religions going back for as long as we have records of religious practices. Whether to allow animal sacrifices today is a difficult choice. Is the fact that dominant religions don't do animal sacrifices anymore a good enough reason to ban it? Is protecting the animals a good reason to ban it?
I think that it's very important to keep firmly in mind the fact that the absence of animal sacrifices in a society's dominant religions could influence us against the practice. In modern America, at least, it would be very easy to regard animal sacrifices as "weird" and "primitive" simply because it's not normal in the context of Christianity or Judaism, but that's not only a poor reason to oppose the practice but is in fact an expression of privilege: treating others and their traditions as "inferior" and "abnormal" simply because they aren't yours or what you are used to.
It's very easy to offer rationalizations as if they were reasonable, logical arguments but which are really just masks for privilege. It occurs all the time in the context of race, gender, sexual orientation, and religion. It's hard for the people enmeshed in privilege or privileged practices to see it for themselves, which makes it all the more important to try when it's clear that privilege may be part of the equation.
In this case, there is a potentially legitimate argument against animal sacrifices -- the treatment of the animals -- but is that a rational argument or a rationalization? One way to determine how genuine an argument really is is to look at whether or not it's based on principles that are applied consistently. So, is the treatment of animals during sacrifices any worse than the treatment of animals raised for food? If not, then are the people arguing against allowing animals sacrifices making the same arguments against modern animal husbandry? If not, then they aren't being consistent and are probably just rationalizing.
This is a good opportunity for you to reflect on your initial reaction to the concept of "animal sacrifices" and what it says about you, your attitudes towards minority religions, and the degree to which even you as an atheist may still be influenced by Christian privilege in modern American society. Atheists tend to be among those who are negatively impacted by the privileging of Christianity and Christian traditions, but this doesn't mean that atheists may not also at times still unconsciously accept attitudes which are dependent on those privileges.