"Believers" was one of a very few Star Trek-style "issue" episodes which dealt with currently relevant political issues, in this case the classic struggle between religion and science, and the right of parents to make decisions for their children.
One obvious connection is with to the religious rejection of medicine often ascribed to the Jehovah's Witnesses. More controversially, and perhaps more interesting, is the connection between this episode and the Judaic practice of circumcision believed by some to go against medical ethics. The aliens in this story believe that life-saving surgery will destroy their son's covenant, a word often used by Jews in association with circumcision. Also, the last scene in the episode shows a family dressed in clothing characteristic of Israeli Jews.