LOUISVILLE, Ky.—Rabbi Chaim Litvin keeps the tools of his work with him at all times: a yarmulke to cover his head; tefillin, small leather boxes containing parchment inscribed with Torah verses; and a pair of goggles, which he needs when he inspects distilleries to certify this state’s signature export, Kentucky bourbon, as kosher.

“I also keep a hair net and beard net in my car,” Rabbi Litvin, 31 years old, said. “If no one had stepped up, there really wouldn’t be much kosher hard alcohol around here.”

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