This could be a good idea, but it needs to be thought out carefully.
Sometimes it happens on its own. An appearance last year by Julio Bocca and his Boccatango company was packed with well-off Latin Americans. The Trocks got huge numbers of gays. Nutcrackers attracts all those well-behaved children dressed alarmingly just like the kiddies on the stage in Act I.
At other times it's planned in conjuction with an outside organization. A major theater company in our town arranged a special peformance of a gay-themed play, along with a meet-the-actors-and-director reception, for members of the local gay and lesbian organization. They have done similiar projects with women's, Jewish, and civil rights organizations.
And then there are all those evenings when the audience gives the impression that there IS a theme night going on, even though no one publiciized it as such:
"Well-Off White People of a Certain Age Night."Who else has spent their lives believing that the classical arts are something you can't live without? And who else has the money to pay for those very high-priced tickets?

P.S.: Papeetepatrick, most theaters already have cell-phone evenings, usually held in conjunction with "Cellophane Candy Unwrappers Night" and "Who Can be the First to Evacuate the Theater As Soon as the Curtain Falls? Night." In our area, small but audible gatherings also help make almost every performance "'Snore Along with the Music Night."