Actually, almost everything on the Met stage is covered by copyright. The instrumental and vocal arrangements, the staging, choreography, sets, pretty much everything but the original source material.
Well, for the classical opera repertoire it would be a fairly weak claim. You don't rearrange say, Mozart, much, if at all. Most opera doesn't really have choreography. It could but basically, it has direction. Set design is most clearly covered by copyright, but it would be difficult to enforce outside of blatant rips of distinctive designs. Clothing and fashion generally can't be copyrighted.
I can't find much about actual lawsuits over these issues on a Google, except the famous Urinetown! case of ought six. This quote is helpful:
In the past, only the work of playwrights, choreographers and set designers has been deemed protected by law, but for direction, and costume and lighting design, the situation is much more fuzzy, Shechtman says.
These quotes from an article on the settlement of that case also make an important point:
New York side of the dispute had the support of directors' union the Society of Stage Directors and Choreographers, which aimed to use the case to boost its longstanding argument for the establishment of a director's copyright on certain staging choices.
The Dramatists Guild of America, which has taken a stance against such a copyright to protect revenues for its member scribes, swiftly touted an excerpt from a Department of Justice intervention in Mullen v. SSDC, et. al, which states "the Register denies that stage direction, as presented to the Copyright Office for registration, is copyrightable subject matter."
It is dead wrong to suggest that the proper action in the case of uncertainty and unsettled law is to sit back, be careful and wait for the court to make an objective decision to determine the Platonic truth of the law. Copyright law is about actors with competing interest pressing their cases, and the accepted practice and facts on the ground do play an important role in deciding where the lines will be drawn, just like the directors and playwrights are jockeying for position above.