One of Hollywood’s leading Native American figures is being accused of faking her claims of Cherokee heritage, The Post can reveal. Award-winning Heather Rae, 56, serves on the Academy of Motion Pictures’ Indigenous Alliance, previously headed up the Sundance Institute’s Native American program and claims “my mother was Indian and my father was a cowboy.” Multiple prior news reports have also cited her as having a Cherokee mother. But a watchdog group called the Tribal Alliance Against Frauds is now demanding the Academy and the producer drop her “false claims” while activists insist she’s at best 1/2048th Cherokee. The group...