When the movie “Free Willy” is released, word gets out that the star, a killer whale named Keiko, is sick and living in a tiny pool at a Mexican amusement park. An environmentalist sets out to give the fans what they want: their favorite celebrity orca back in the sea.

After the movie “Free Willy” became a hit, word got out that the star of the film, a killer whale named Keiko, was sick and living in a tiny pool at a Mexican amusement park. Fans were outraged and pleaded for his release. “The Good Whale” tells the story of the wildly ambitious science...