I've seen two plausible suggestions. One, many of Hollywood's most influential figures were raised in Christian Science, such as Elizabeth Taylor and Marilyn Monroe, or converts to it, like Mary Pickford. Hollywood is a close-knit group, so it shouldn't be surprising if three's a little evangelism going on, just as there is with Scientology.
The other suggestion was that it became popular to associate with Christian Science during the Red Scare: without requiring particular religiosity, it was sufficient to avert charges of atheism, and hence Communism.