The robust return of “Roseanne” has made the show and its namesake star political lightning rods. Fox News pundits joined Mr. Trump in hailing the success of the “Roseanne” premiere as a victory of their own. Some viewers on the left have expressed misgivings about supporting the show. And there were hot-take commentators who argued that “Roseanne” is surprisingly subversive, with more nuanced politics than either its ardent fans or its vocal detractors have acknowledged.

The third episode was about a generational parenting conflict that pitted Roseanne’s stricter, more traditional style against the looser, hands-off approach of her daughter Darlene.

A wild card factor is how much of a ratings drop will come in the show’s third week. Will “Roseanne” suffer mild, 5-to-10-percent declines as it moves closer to its ninth and final episode? Or will the falloff be steeper?

To make matters more complicated, Ms. Barr has her Twitter feed back.

Two months before the show premiered, she was not much of a presence on Twitter. She said her family had taken her password away, and she mentioned that she did not “want it to overshadow the show.”

But in recent weeks, Ms. Barr has been posting frequently on Twitter, and it did not take long for her to stir up controversy. Over the weekend, she seemed to endorse a fringe conspiracy theory known as “The Storm,” which suggests that Mr. Trump is breaking up child sex-trafficking rings involving Democratic politicians.

The message, which was later deleted, raised questions about whether Ms. Barr might eventually cause a revolt among viewers or advertisers, a cause for some concern among ABC executives, who have publicly backed their reborn star.

“You can’t control Roseanne Barr,” Ben Sherwood, the president of Disney and ABC’s television group, said in an interview last week. “Many who have tried have failed. She’s the one and only.”