Well, there is always a significant possibility of visitors feeding their alcoholic refreshments to the animals. As you may or may not know, many zoo visitors don’t obey the rules or the signs, and when beer is involved, that can get dangerous in a zoo setting.
I don't think that's much of a concern. The purpose of beer gardens is to limit where it's served, so people aren't just walking around with alcohol. I rarely see them open, and even when they are, usually don't see anyone getting anything.
I've been to one zoo event where alcohol was a big feature, and it was the *employees* that were having concerning behavior, not the visitors (do I even need to say it wasn't an AZA place?)