There always seems to be one high maintenance person in a group like this, but it's been my experience that they eventually stop coming. With any luck that will happen in this case too.
I worked with a high maintenance woman like this. Each of us would bring a cake (or some other kind of treat) on our birthdays. Everyone would enjoy it. The high maintenance woman told us she wouldn't bring a cake because it was unfair we were taking advantage of her. Someone pointed out to her that she always ate the treats that other people brought in so how were we taking advantage of her? She said it was unfair. We quit doing it.