On the opening night for “Crazy Rich Asians” in China last Friday, 25-year-old graduate student Hu Lianyu went to catch the movie that has won big audiences in America.

There were only a half-dozen people in the theater in the southeastern city of Ningbo, and the film left him feeling perplexed. “It was very light-hearted,” Mr. Hu said, but he didn’t like how it portrayed wealthy Chinese people as “having old-fashioned thoughts and behaviors that are in poor taste.”

“Crazy...