"Many 20- and 30-somethings here have theater backgrounds, for example, and often say it's inappropriate to wear jeans to theater...."
I always hated that expression "to theatre"... It just wreaks of snobbery. It's like "oh muffy, where do you summer?" Never saw either of those words as a verb, I guess??
Well, I've never heard that use of the word theater either. However, it's a completely appropriate use of summer. Summer does have a verb form, and has since antiquity.
"Theater" is being used as an adjective in this sentence, modifying "performances": "... to theater (performances) and other cultural performances ..."
It's kind of an awkward construction, but at least it's not, "I'm going to theater; are you coming with?"