“Finding Your Roots” has become a phenomenon, attracting celebrity guests from Samuel L. Jackson to Anderson Cooper to Gloria Steinem — and it all began with host Henry Louis Gates Jr. receiving a piece of angry fan mail.

“When I first started the series in 2005, I only did African Americans,” Gates, 69, tells The Post. “We started with Oprah and Quincy [Jones] and the reaction was so electric, PBS immediately asked me to do another special … Then a lady of Russian Jewish ancestry wrote to me and said she’d always admired my stance on cultural diversity, but after watching the show, which was called ‘African American Lives’ she’d decided I was a big fat racist, because I only did black people. She said, ‘What about people like me, from eastern Europe? What about Asian people?’”

That idea eventually became “Finding Your Roots with Henry Louis Gates Jr.” Now in its sixth season (Tuesdays at 8 p.m.) the show traces the genealogy of celebrities, from politicians such as John Lewis to authors such as George R.R. Martin. Each episode sees two to three different guests learning about their family history, with help from Gates.

“My day job is I’m a professor at Harvard, and my goal is to teach my fellow countrymen and women as much about American and world history as we possibly can. There’s no easier, more fluid way to do that than by telling the stories of the ancestors of entertainers or politicians or well-known people about whom the public is fascinated,” he says. “We deconstruct ethnic identities to show that when the lights came down, everyone was sleeping with everyone else — that’s the way human history goes!”

Gates attributes this instinct towards uncovering people’s personal stories to his childhood in West Virginia, spent with parents with a flare for telling tales.

“My father was a great storyteller, my mother actually used to write the obituaries for all the black people in the Potomac Valley in eastern West Virginia,” he says. “So I was raised with a writer and a storyteller. The greatest way to educate is to make the lessons palatable, and there’s no way to make them more palatable than by good storytelling. People stop me everywhere I go — airports, on the street, they’ll come up and say, ‘Can I have a selfie? I love ‘Finding Your Roots’!”

Of course, some of the information uncovered by “Finding Your Roots” is sensitive — and Gates says there’s a protocol he follows behind the scenes. For instance, when Todd Smith (aka rapper LL Cool J) appeared on the show in 2016, Gates and his research team discovered that Cool J’s mother was adopted.

“I had to call him. We have a protocol for telling people about what are called ‘non-paternity events,’” Gates explains. “If you’re a guest and your father wasn’t your father, I can’t tell you that in front of 2 million people [on camera]. I have to tell you that privately, and then you decide if you want to stay in the series or not. If you stay in the series, we have to reveal that.”

This season’s guests on “Roots” include Sigourney Weaver in Tuesday’s episode. “Mrs. Maisel” star Tony Shalhoub will appear in a future episode, as well as “Watchmen” creator Damon Lindelof and his stars Regina King and Jean Smart.

Gates knows that latter trio thanks to a cameo he had in the HBO drama. When Lindelof approached him about a small role, Gates initially declined.

“I go, ‘What? I’m busy, I’m making PBS films!’” Gates says. “He kept writing to me and finally we had dinner and he said, ‘Your work on the Tulsa riots in 1921 … contributed to the plot.’ Now, here’s an example of how a history series on PBS helped to shape popular culture. It was great. We shot my scene, I didn’t know how it would fit in until they sent me a link a day before it was about to air, and then I see Regina King come up and talk to me and I’m a hologram. It cracked me up. I figure turnabout is fair play — we’re going to have an all ‘Watchmen’ episode [of ‘Finding Your Roots’].”