STAMFORD, Conn.—After watching the world-renowned Shen Yun Performing Arts, Don and Carolyn Chiodo had an important takeaway message. “I think that people should actually come to performances such as [Shen Yun], not just to see things that are beautiful, but also expand their learning and their mind,” said Mr. Chiodo. The couple had been enjoying the performance at The Palace Theater in Stamford with a friend, a retired school teacher. Mrs. Chiodo is a flower designer and owns her own business. “I loved learning about the [Chinese] culture. I’m not familiar with it and didn’t realize how much religious symbolism [there was]. It was enlightening,” she said. “I like the pageantry and the dance and the music—the music is wonderful,” said Mr. Chiodo, an executive director for JP Morgan. The dances tell stories from China’s five millennia of history, stories that are steeped in traditions that have been passed down …