The era of binge-watching hasn’t just changed the way we watch television: It’s changed the way we react to it, as well. When Netflix or Amazon makes a whole season of a show available at once, as Netflix did last week with “Unbreakable Kimmy Schmidt,” a new show from Tina Fey and Robert Carlock about a cult survivor (Ellie Kemper), the entire critical life cycle seems to happen in a single weekend, rather than over a period of six or nine months. In the case of “Unbreakable Kimmy Schmidt,” the cycle started with wild praise, then moved on to more sober assessments, including a number of critiques of the show’s racial politics.

Among them was my friend Libby Hill’s essay on one of the series’s many surreal choices, the decision to reveal that trophy wife Jacqueline Voorhees (“30 Rock” veteran Jane Krakowski) was in fact a Lakota woman passing for white. Cross-racial casting is a justifiably controversial practice. And in her piece, Hill suggests that Carlock and Fey’s invocation of the Native American writers on the “Unbreakable Kimmy Schmidt” as inspiration for Jacqueline’s backstory “reads like the rough equivalent of, Well, I have Native American friends.”

For clarity’s sake, this is how the two explained the choice at the Television Critics Association press tour. “We actually have a couple of writers on staff with Native American heritage. One of whom had spent a year on a Lakota Sioux reservation, and so we felt like we had a little room,” Carlock said. “And a resource,” Fey interjected. “To go in that direction,” Carlock continued. “And then we found these two great Native American actors to play Jane’s parents, who are just hilarious.”

Following that thread, I asked Krakowski if she’d worked with the writers in developing Jacqueline as a character.

“I think their collaboration is much more with the other writers in the writers’ room and their wanting to be proper about it. We’ve been very strict to the Lakota traditions and all of that,” she explained. “I actually speak some Lakota in the episodes coming up, and they come down and practice with me, and we treat it with the proper reverence that we want to salute that community with.”

I was also curious about whether Krakowski had concerns about playing a non-white character who is passing as white.

“I have such creative trust in Tina and Robert Carlock, that I trust wherever they bring me,” Krakowski said. In “30 Rock,” that included an episode where Jenna Maroney donned blackface to tweak her co-star, Tracy Jordan (Tracy Morgan). “Certainly in ’30 Rock’ they created such a farcical land that we lived in that we were protected in that bubble, that we were able to go to such a farcical level that it didn’t seem to go to reality, it didn’t leave the bubble of comedy, which was fantastic . . . Jenna didn’t seem to know right or wrong or anything outside her own world, so it gave her the freedom to be wrong, all the time, to an extreme level. It’s a great creative freedom place to be in.”

None of that means you have to take Fey, Carlock and Krakowski’s words for it — art has to stand on its own once it goes out into the world, and if it doesn’t communicate what its creators intended, their intentions are no defense. But it does seem like a stretch to suggest, as Hill does, that the among the staff and cast of “Unbreakable Kimmy Schmidt,” “nobody thought it would raise alarms at all.”

For what it’s worth, I see Jacqueline’s story differently than Hill does. Jacqueline’s behavior when she decides to embrace her Native American heritage is ludicrous. But she’s ignorant and acting out stereotypes less because she was denied her culture by white oppression but because as a bratty teenager, she constantly blew off her parents. And faux-Native American schtick is plenty worthy of criticism. It’s Jacqueline’s obsession with white culture that’s absurd — “Jackie Lynn is a cheap stripper name. Jacqueline is a classy stripper name,” she tells her parents when they come to visit her in a flashback — not anything about Lakota culture as represented by her parents.

But Hill’s critique raises an important question for people who want to advocate for diversity in television. On the face of it, Fey and Carlock have done exactly what they were supposed to. They hired people of color to write on their show, and rather than set them to writing exclusively white characters, they changed the show to provide more outlets for their staff’s expertise and life experiences.

The fact that their efforts didn’t land for some viewers adds an uncomfortable footnote to the debate about diversity in pop culture. Whether it’s Fey and Carlock hiring Native American writers, or Lee Daniels — who some viewers see a promoter of certain images of black pathology — producing a smash hit like the hip-hop drama “Empire,” someone’s gender or skin color doesn’t guarantee what kind of story they’ll write, what kinds of characters they’ll create and what kind of jokes they’ll tell.