Her Children’s Television Workshop brought together educators and entertainers, including a puppeteer named Jim Henson and the director Jon Stone, an idealist attracted to Cooney’s idea of closing the literacy gap for inner-city Black children. “I think what drew Dad in really had to do with her political vision,” his daughter Kate Stone Lucas says in the documentary. (Stone died in 1997.)

As “Street Gang” lays out, the show’s very setting — a city street, not a fantasy castle or picket-fenced house — said something about the range of children it sought to welcome. The racially diverse cast of grown-ups and kids said something. “Sesame Street” was open and public and real, as real as a block where humans hung out with furry monsters could be.

“I saw it as a political show,” says Sonia Manzano, who played Maria, because of its casting and its determination to raise conversations that kids’ TV wasn’t used to having.

Matt Robinson, the first actor to play Gordon, voiced the ’70s-era Muppet Roosevelt Franklin, who was created to represent Black children in the audience. The singer Buffy Sainte-Marie nursed a baby while explaining breastfeeding to Big Bird. The Rev. Jesse Jackson led kids in a call-and-response of “I am somebody!”

Big Bird, whose character evolved early on from a goofy oaf to a curious child, has often been the young audience’s surrogate, just as he was when he offered up a wing to teach kids about the vaccine. The most memorable and moving example came when Will Lee, the actor who played the shopkeeper Mr. Hooper, died. The show wrote the death into an episode, in which Big Bird learned that when people die, they don’t come back.

Out of the box, “Sesame Street” was a rara avis: a mass-market hit on public TV, a kids’ show with sophistication and a wild countercultural energy. It even surprised the people who made it.

“We’re shooting this show, and you see this ugly bird,” the cameraman Frank Biondo says in the documentary. “I remember thinking, ‘Who’s gonna watch this [expletive brought to you by the letter S]?’”

But it was not universally loved. A Mississippi state TV commission refused to air “Sesame Street” after complaints about the racially integrated cast. Local commercial affiliates picked up the show, knowing a hit when they saw one, and the board eventually reversed the vote.

It’s easy today to feel superior to this racial history, or to forget it. When Sesame Street introduced a Korean American Muppet this year, Matt Schlapp, the president of the Conservative Political Action Committee, called the addition “insane” on Twitter. “I grew up watching, and it was never about race,” he said on Fox News. (Someone inform Roosevelt Franklin.)

“Street Gang” cuts off around the end of the Jim Henson era (Henson died in 1990); Elmo gets just a fleeting glance, and decades of history, including the move of the flagship show to HBO, go unnoted. So the documentary doesn’t examine the show’s cast and format changes, or the question of whether it would or could have been created today, in an era of many more TV options for children (albeit more commercial ones).

But as culture-war skirmishes like Cruz’s show, more has changed since “Sesame Street” began than the number of TV outlets. The L.B.J.-Nixon era that gave us the show was polarized too, yet the series reflected at least some 20th-century consensus about the role of institutions, from government to medicine to TV networks. It was not outlandish that Washington would take a role in teaching kids through the country’s most popular mass medium. (Senator Barry Goldwater of Arizona, once an arch-conservative presidential nominee, was one of the most potent early defenders of “Sesame Street.”)

Now, in a time of fractured media and politics, characters from an HBO Max show do a CNN vaccination special that gets zapped on Twitter by a senator looking to score points with the Fox News audience. It’s a bigger media universe than when “Sesame Street” first tried to cram the whole world into one block. But we live in smaller and smaller neighborhoods.