The ratings system for movies is not mandatory. Films can be released with no rating, but mainstream producers know that a film with an MPA rating will have a better chance of being shown in theaters and selling. You will often see how DVD releases of films sometimes include unrated versions on the DVD, so that the purchaser can enjoy the uncensored version of the film that the director intended.
The closest you’ll get to the MPA with theatre is The Broadway League, and that organization is largely composed of producers who most likely would be against censorship of any kind. It would also be a conflict of interest for competing producers to be voting on rating each other’s shows.
When considering the rating of theatre in general, Broadway represents a very small fraction of what is produced in the world every day. When a film is rated, there is just one film, and it’s shown in its original form all over the world. Right now, there could be hundreds of productions of “Hamlet” and “Godspell” happening simultaneously, and each one of them is different than the other. While the actors are required to speak or sing the same lines, the details of the set, costumes, and stage directions will be different, and one production might be a lot more risqué than another. So, should it be the script, not the production that receives the rating, because no ratings organization would be able to run around the world watching the final dress rehearsal of every single play being produced to determine a rating before opening night. Sounds sensible, right? However, what happens when the script for “Our Town” receives a G rating, and a mom decides to take her two young kids only to discover that the play is being performed in the nude? So, rating the script doesn’t work, either, because of the flexibility that is inherent to how plays are interpreted and produced.
The bottom line is that parents are responsible for the situations in which they put their children, so they should do some research beforehand. Had the parents who had to leave “Waitress” with their young children Googled “Is Waitress appropriate for children,” they would have immediately seen a link to a thread on the Broadway World Forum which would answer the question. If more people started taking responsibility, then less people would have to tell them what to do. Less, not more censorship is always better when it comes to freedom and autonomy.