To defend and burnish Tulsi Gabbard’s image as her political star was rising, her congressional campaign hired a public-affairs firm in 2017 that tried to suppress coverage of an alleged pyramid scheme connected to her Hindu sect, according to interviews, emails and Federal Election Commission records. Gabbard, a former House member who is now President Trump’s nominee for director of national intelligence, was raised in the Science of Identity Foundation, a sect tied to a direct-marketing firm accused of running a pyramid scheme in several countries. Neither Gabbard, the sect nor the firm, QI Group, wanted the relationships scrutinized. Gabbard’s...