But by general cultural and sociological standards, yes J. D. Salinger was half-Jewish because his father was a Jew. Moreover, Wikipedia reports that, "Salinger's mother changed her name to Miriam and passed as Jewish. Salinger did not find out that his mother was not Jewish until just after his bar mitzvah."
JTA reports, "The author was born in New York in 1919 to an assimilated Jewish father and a non-Jewish mother of Irish descent. Salinger's father, Sol, was the son of a rabbi. He worked as an importer of ham and tried to get his son into the business, according to The New York Times, but the younger Salinger instead became a writer."
After 1946 in New York City, some reports say that Salinger studied Zen Buddhism. In later life he lived as a recluse in New Hamshire. He was eclectic in his religious life, at times a practicing Hindu, and a variety of fads and cults at other times, per Wikipedia,
After abandoning Kriya yoga, Salinger tried Dianetics (the forerunner of Scientology), even meeting its founder L. Ron Hubbard, but according to Claire he was quickly disenchanted with it. This was followed by adherence to a number of spiritual, medical, and nutritional belief systems including Christian Science, homeopathy, acupuncture, macrobiotics, the teachings of Edgar Cayce, fasting, vomiting to remove impurities, megadoses of Vitamin C, urine therapy, "speaking in tongues" (or Charismatic glossolalia), and sitting in a Reichian "orgone box" to accumulate "orgone energy".Salinger died today at the age of 91.