Here is a statement from the MTI website covering videotaping (I couldn't find a statement on photography).
"Copyright law gives authors the exclusive right to control the reproduction of their work. When MTI grants a license for a live stage production of a show, that license does not include the right to tape it because the authors retain the sole right to decide when or if their work is recorded in any way. Even a videotape made for classroom use, as a personal memento or as an archival school record violates the authors' separate right to reproduce their work. In many cases, the authors have already granted such rights exclusively to film or television companies, in which case you would also be infringing upon the rights granted by the authors to a third party."
In another section discussing changing a musical in any way, they state:
"It's important to remember that under Federal copyright law, not only can the director or producer who decided to change the work be held liable, but the entire production staff, cast and crew -- even the owner of the building, can be held liable, whether or not they knew they were part of a willful violation of copyright law"
Now, I have done a number of community theater productions. Almost all were videotaped at some point. All (100.00%) were changed in some way. These changes usually involve cutting some of the musical numbers (e.g. taking out a repeat, adding a repeat, removing a difficult dance sequence...).
It would make sense that one could make photographs for the promotion of the particular production. I.e. for programs, lobby photos, newspaper stories, etc.. However, I don't see those rights spelled out.