NEW BRUNSWICK, N.J.—Audience members at the State Theater New Jersey experienced a performance as profound as it was mesmerizing on the evening of Nov. 21, as Shen Yun Performing Arts staged its last performance of the weekend after a three-show run at the theater. Francis McEnerney,  a partner at an accounting firm, said Shen Yun took his breath away. “It was absolutely magnificent,” he said. It was Mr. McEnerney’s first time attending Shen Yun, the Chinese classical dance and music production sweeping the world with its annual global tours. Based in New York, Shen Yun brings to life Chinese culture as it was for millennia before communism. “The stories were the best part. In the beginning, we saw a lot of dancing, but towards the middle and the end, it was a lot of stories,” Mr. McEnerney said. He added that he was very impressed with the animated backdrops used in the different dance …