Jonathan Ichikawa has an interesting argument for vegetarianism. It would be immoral to have a party where we throw human parts around just for the fun of it, parts from people grown specifically so that we can have enjoyment in doing exactly that. Jonathan suggests that it would be wrong to attend the party even if such attendance doesn't cause the practice or fund it in any way. He says this is because it supports it. I'm not sure that's the real reason it's wrong. I agree with Richard's comment that mere participation in an evil practice is wrong. I don't think it's supporting it that's the issue. It might be ok to support an evil practice as long as one's reason for doing so is not to use that evil practice as a means to your end but rather that the support is an unintended side-effect that your end doesn't itself rely on. But in this case that's not what's going on, since you're actively participating in the practice. That's what seems to me to be wrong about it. Is the same true for eating animal meat produced in factory farms? The argument assumes that animals in factory farms really are treated immorally, but that's something I agree with.
One way to distinguish between the two cases is if you have a basic distinction between our moral obligations to animals and our moral obligations to humans. Some people, for instance, think we have moral relationships with humans as our fellow members of a moral community that we don't have with animals. This doesn't mean we have no moral obligations toward animals, but the fact that they're not in the moral community with us in terms of being moral agents themselves is, on some ethical theories, reason for taking them to have moral properties of a different order. Perhaps this is not having rights of the same sort. For example, it's easier for our obligations to animals to be outweighed by other considerations than it is for our obligations to humans, or perhaps our obligations to humans can never be outweighed, while our obligations to animals can.
I don't myself think this is sufficient, because I think attending such a party with animal parts is immoral (even if you don't pay to attend). I do think it's much less wrong than with people parts, but it's wrong. The reason is not that you're funding the killing of animals for mere entertainment (although if it's also that, it might add to its wrongness). It's also not that it's merely supporting such a practice. You're engaging in the very entertainment goal that constitutes the evil practice. You're not merely supporting it, and I think engaging in it without supporting it is wrong. Suppose, for example, that you were able to sneak in, take an animal part or two off to your own private room with some friends, and engage in your own game of catch for enjoyment. I don't see how that provides any support for the practice. You even detract from it by stealing some of their animal parts without ever engaging with those who are doing it in any positive way. But you participate in an important way in the behavior that constitutes the practice.
So I don't think this is the right way for those who defend meat-eating to respond to Jonathan's argument. Merely distinguishing between the moral status of humans and animals won't be sufficient if the same practice with animal parts is wrong, and it's wrong merely to participate in it. If eating meat is analogous to playing games with it, then merely eating it is wrong. That's participating in it. It doesn't matter if you aren't providing any noticeable (or even any) support to the practice that will help it continue or fund those who do it. Even if you stole all the meat you eat, you'd be participating. So I think defending omnivorous practices in a world where most meat comes from factory meat-market is going to require finding some disanalogy between the case of eating meat and the case of throwing animal meat around for entertainment.