No, Judge Jay Bybee is not a Jew. Bybee is a Mormon, a member of the Church of Jesus Christ of Latter-day Saints.
Bybee graduated from Brigham Young University and earned his Juris Doctor from BYU's Law School.
On April 16, 2009, President Barack Obama released an internal memorandum signed by Bybee during his tenure at Office of Legal Counsel of the United States Justice Department addressed to CIA General Counsel John Rizzo and dated August 22, 2002, which concluded that waterboarding did not meet the legal definition of torture ["Bybee memo"].
On April 19, 2009 an editorial in The New York Times ("The Torturers’ Manifesto") argued that Bybee is "unfit for a job that requires legal judgment and a respect for the Constitution" and called for Bybee's impeachment from the federal bench.