A professional theatrical production of Phantom of the Opera means actors' getting paid. The theater is their workplace and showing up in a shorts, tank tops or even ragged jeans is a sign of disrespect. This goes for all theatrical productions, but is especially so for Phantom of the Opera because the musical is filled with characters in extravagant costumes and elegant dress.
The opera is one of the few places left where people are expected to show up dressed up. Phantom of the Opera is not an actual opera, so you need not arrive expecting the kind of formality that is applied to that particular medium. However, there is much about the musical that contains elements of opera so try to find a happy medium between the highly formal dress expected at an opera and the less formal dress typified by a standard musical.
When attending an amateur production of Phantom of the Opera, or even a professional production at a small theater, a more informal style is acceptable. This means dark jeans that are not ripped and a nice button down shirt or blouse. Men should ideally wear the kind of sports jacket that goes with jeans. You should not wear a T-shirt unless it is a classy Phantom shirt and then only with a jacket. The shirt should also be tucked in for a less sloppy look.
The best clothing to wear to a production of Phantom of the Opera is something dressy that matches the ambiance of the production. For women this means an elegant black dress for women and a nice dark suit for men. Phantom of the Opera is a fairly long musical, which means you can expect to be sitting still for a few hours. For this reason, make sure the dress or suit is made of material that breathes.
You might be tempted to wear a costume to Phantom of the Opera. This is not a good idea. You can forget about wearing the iconic Phantom mask as this will likely be deemed a security risk before you even get inside the theater. While a cape may seem like something fun to wear, keep in mind that you will need to remove it before you sit down or else run the risk of slightly choking yourself as you sit back on it when you take your seat.