What an interesting topic. I am curious, what exactly do you expect her to do with all the cards she gets at each swap? I don't do swaps regularly, but if I did, I am not sure what I would do with all the cards. I also don't think I would participate with a swap if there were strings attached to what I could do with them after the swap.
I believe that once you give something to someone else there should not be strings attached and everyone has their own code of ethics and rules that they live by. They should be able to do what they want with the items they receive based on their rules and code of ethics. You have a right to react and feel the way you do because you would not do that based on your code of ethics. Everyone is different as is obvious by all the differing opinions here. I don't think there really is a right or wrong answer here, just different opinions.
You say you were at a church event. I am not sure if that means you are a Christian attending the church or if you were just visiting for an event. If you are a Christina attending the church you may be familiar with the advice given in the Bible. When you have an issue with a brother or sister in the church you should first address it with them. If it does bother you so much that you feel you must do something. Then the best thing to do is to approach her one on one and talk to her about it. Honesty and facing the person directly is the cleanest way to handle any situation. Not necessarily the easiest. After you discuss the situation and if she still wants to handle the swaps differently than you wish her to. Then maybe you need to find out if the rest of the group agrees with you. And if yes, then you may need to ask her to leave. Again, not the easiest solution. But laying it all out and addressing the situation is better than just talking to others about it. She may have no idea you think it's wrong and that you are offended by what she is doing.
I pray it all works out for you and you are able to choose the best way to handle the situation.