I started to introduce classical music to the kids early on. The first performance they saw (4.5 and 2.5 YO) was the Nutcracker. I bought tickets in a side box where there was a door if we had to leave during the show. Because of the dancers, story (which they knew) and general decor, they didn't move a muscle.
The symphonic orchestra in my town has a children's series. The pieces are upbeat, short and fun. They are also paired up with something else. For "Le Carnaval des Animaux", the local zoo brought some of their animals for the kids to learn about. I also learned that petting a snake is nice (never too old and such). Later, my son was able to watch a whole opera on TV sitting quietly beside me.
So, yeah, you can bring a child to cultural events, just make sure you can 1) get out without fuss if need be, 2) that it's age appropriate.