I have a story about the "no animal products at the altar" rule:
Some years ago, my priest was visiting a Coptic church where he came across a kind of incense with a really beautiful smell. The name of it was "gold musk," and he later asked me if I could track it down for him, since I run the church bookstore.
So I did a search and found it at a place called Cal-Hellas, in Cuppertino, CA. After I found it, I wondered what the word "musk" referred to. So I looked it up on the internet and read something that led me to believe that it came from a dear that's been killed.
Immediately, I thought of Bambi and his mother. I was really disturbed by the thought of a poor dear being killed to make incense. So I called the guy at Cal-Hellas back and asked him about it. Upon hearing my concern, he laughed. I can't recall his exact explanation of what the "musk" in the incense was, but he assured me that no deer was used in its making. And as part of the explanation, he told me that if it came from a deer, it wouldn't be allowed at the altar, since animal products are not allowed there.
Now this guy is Eastern Orthodox, so I assume the rule about no animal products must apply to EO Churches too. It's not just an OO thing.