NEW YORK — A Liberian woman accused of smuggling endangered monkey meat from Africa to New York has failed to persuade a judge that she shouldn’t be prosecuted because she needed the butchered carcasses for religious reasons. Mamie Manneh ran into legal trouble three years ago when customs agents seized a shipment of dozens of primate parts, hidden in a batch of smoked fish, as it passed through Kennedy Airport. The dozen boxes containing the skulls, limbs and torsos of monkeys and baboons had been shipped from Guinea and were headed to Manneh’s home on Staten Island. Agents who searched her house found 33 more animal parts in her garage. Manneh was charged with smuggling the meat of two endangered species. As her case moved toward a trial, her lawyers argued that she and other immigrants in Staten Island’s thriving community of Liberian Christians ate monkey meat for spiritual reasons, particularly during holiday celebrations, and were thereby protected by the First Amendment an