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Ever since he announced his bid for the presidency, Donald Trump has capitalized on the news and entertainment media, dominating coverage with a mixture of hyperbolic pronouncements and theatrical flair.

But after his proposal to halt Muslims from entering the United States earned a sharp rebuke, including condemnation from some of his Republican rivals, the ratings bump that Trump promises seemingly carries with it an extra degree of incongruity.

While it’s one thing for news shows like “Morning Joe” and CNN to book Trump to defend his proposal; it’s another for entertainment shows to showcase the softer side of the candidate, via light comedy as he has done on “Saturday Night Live” and “The Tonight Show Starring Jimmy Fallon.”

The latter shows have become an increasing part of presidential campaigns, as candidates try to reap the rewards of an often friendlier atmosphere and coming across as more personal and more likable.

But what is the responsibility of “soft” talk shows if their subject has been called out as a bigot by more than a few critics?

On Wednesday, Trump is scheduled to appear on “Live! with Kelly and Michael,” which has been featuring 2016 candidates in a relaxed format that has been otherwise reserved for light chatter with celebrities, a pre-candidate Trump included.

The interview was scheduled weeks ago, before he made his Muslim proposal, and is still scheduled, according to a spokeswoman for the show. If it ends up happening, it will be interesting to see how the show navigates its softer tone with an ever-more polarizing figure.

“At this point, booking Trump on a late-night show to engage in amusing banter would be incredibly irresponsible,” said Dave Berg, who was co-producer of “The Tonight Show with Jay Leno” and tasked with booking political guests.

“Trump’s plan to bar all Muslim immigrants and tourists from the United States goes beyond his typical tendency to make outrageous remarks,” Berg said via email. “It’s a fascist idea.”

Some of Trump’s Republican rivals have condemned his remarks. Jeb Bush, for instance, called Trump “unhinged.”

The Huffington Post, which had relegated Trump to the entertainment pages, announced on Monday that it was shifting him to the news section, while calling him out if his words are racist or sexist. Arianna Huffington announced the change in a piece entitled “A Note on Trump: We Are No Longer Entertained.”

Tom Brokaw, meanwhile, did a segment on “NBC Nightly News” on Tuesday in which he said that Trump’s comments fed into the fear and paranoia that terrorists seek, going so far to say that ISIS is “likely to use Trump’s statements as a recruiting tool.”

Yet he’s been a proven ratings magnet well beyond news channels, in daytime and late-night, on “The View” and “Extra.”

Even before Trump made his proposal, however, his appearances did not always come without acrimony. Latino groups picketed NBC when he hosted “Saturday Night Live” on Nov. 7, and even some members of Congress protested that the network gave him a such prized perch after severing ties with him during the summer. The network also had to compensate at least five of his rivals in the form of free airtime on a number of affiliates, in order to fulfill requirements of equal time laws.

Univision, meanwhile, last week pushed back at Trump’s $500 million lawsuit for dropping its plans to telecast the Miss Universe pageant, then owned by the Trump Organization. The Spanish-language media conglomerate contends that Trump’s statements about Mexican immigrants diminished the value of the pageant and that it couldn’t risk offending its viewership by airing it. Trump’s attorney says that Univision willfully breached its contract and acted in bad faith.

Robert Lichter, director of the Center for Media and Public Affairs at George Mason University, says that while there is a “substantial audience for this kind of red meat, and the more media and political elites denounce Trump for such proposals, the more that audience is convinced that he’s the outsider America needs to take on the gutless establishment.

“But that’s not the same audience that wants a little politics served on their presidential platter. Talk radio, yes. Late night talk, no.”

Lichter and his team monitor late-night humor, and he predicted that “the number of Trump jokes will rise, the knives will be sharper and the cuts deeper.

“As a late night guest rather than a target, he’s more problematic. Neither [Jimmy] Fallon nor [Jimmy] Kimmel has given any indication of wanting to play Edward R. Murrow. Banning Muslims isn’t really material for slow jamming the news.”

He said that there could be opportunity for Stephen Colbert, as the most “overtly political and liberal” of all the nightly talk hosts, to take on Trump. That would give Colbert “the patina of seriousness that Jon Stewart developed, while making him a liberal hero in the bargain. But it could also push him out of the more mainstream image that he has clearly cultivated to broaden his audience from the Comedy Central days.”

For his part, Trump showed little sign of backing away from his proposal, which has once again kept him atop the political news cycle.

He even retweeted a comment from one of his frequent critics, Rupert Murdoch, who seemed to give him some leeway.

“Has Trump gone too far?” Murdoch wrote, “Regardless, public is obsessed on radical Muslim dangers, Complete refugee pause to fix vetting makes sense.”