The nation’s oldest and most fabled secret society, the Freemasons, is going public after more than two centuries, and some of its more traditionalist members are shaking in their sheepskins. Faced with a dwindling membership, the society — whose past members include 28 of the 40 signers of the Constitution — decided to relax admission standards. “It’s an insult to the people who are in it,” Jerry Czin, a Mason for 30 years, said. “I don’t believe in going down to a lower denominator.” “You want to set standards,” Mr. Czin said. “I don’t even like the fact that every...