I once wore a sequined shirt to the theater (to dress up) and wound up with a front-row seat. Throughout the play's first somber scene, I kept wondering why the director would want tiny sparkles of light to flit erratically over the rear wall of the stage and characters' faces. Luckily, I realized my faux pas fairly quickly and donned&zipped up my jacket at the first applause break.
So aside from jangly jewelry, perfume, and overly revealing clothes, we can add sparkly garments to the list of what not to wear to the theater. Other than that, keep your phone off and refrain from speaking, singing along, leaving and returning multiple times, starting fistfights, eating, rustling chip or candy bags, and shaking ice in those godforsaken cheap souvenir cups, and you may wear whatever you please.
That said, when I saw the "Mary Poppins" tour in Boston, I got lost on the way from the T to the theater, and as I looked around for someone to ask directions, I spotted a gentleman (late 30sish) and two little girls: the girls were in party dresses and the gentleman was in a suit. I instinctively knew this little family was going to the theater. Turns out, we had both gotten out at a premature stop and were about 1.5 miles away. The family let me walk with them all the way there (I'm a female and at the time was in my 20s. I'm also tiny and unthreatening-looking, so that likely helped). I was wearing a simple but elegant black dress and gold chain. When we arrived at theater, having chatted about all the shows the family had seen and the girls' opinions on them, I asked the father how he knew I was safe to walk with for such a distance with his daughters. The gentleman said, "Anyone in this day and age who dresses up for the theater like you did has to be all right in my book." So there is that, as well.