I would assume except for the possibility of "R" rated and definitely "NC-17" rated movies, the theaters will allow for the parents to make that decision. I think in many cases families cannot find a babysitter because going to the movies is expensive!
If anyone feels that maybe a PG-13 movie is inappropriate for their child(ren) then there are two good websites that go over all the issues. IMDB has a pretty extensive parent guide for each movie listed (Man of Steel link below):
The Dove Foundation is Christian (and conservative) based and very extensive as well: (Man of Steel link below). The reviews are IMHO pretty good and go over the good, bad and the ugly. A lot I agree with but some of the issues they have with certain movies are petty - but that is their POV and MO. BTW Man of Steel was not approved.
One drawback with the guides is the possible spoilers revealed - in case you haven't seen the movie and want to be surprised.