Is Fox News, like the Republican Party, having moral qualms — or at least nagging concerns — about its image?

It takes a lot to get bumped off the air at Fox News. Just ask one of the network’s star hosts, Tucker Carlson.

He’s still there after calling women “extremely primitive” and Arabs “semiliterate primitive monkeys.” And those are tame examples of the unprintable lines from the audio clips — things he said this century — recently unearthed from his run as an occasional guest on the “Bubba the Love Sponge Show.”

In the age of Trump, Tucker Carlson’s ship has come in at Fox News »

The suspension of host Jeanine Pirro over her incendiary remarks about Muslim congresswoman Ilhan Omar, however, may be a sign that the network, like the Republican party, is starting to have some moral qualms about itself. Or at least some nagging concerns about its image.

Lachlan Murdoch, Rupert’s oldest son, this week officially became chairman and CEO of Fox Corp. after the completion of Disney’s acquisition of 21st Century Fox. But unlike his father, Lachlan is reportedly not a friend or fan of the Trumps, although he hired Hope Hicks, Trump’s former communications director, to be the new company’s chief spokeswoman.

While Republicans have largely been in lockstep with Trump, in a dance to distance themselves from the Washington establishment, the news network that’s been politely characterized as having “a symbiotic relationship with the president of the United States” appears to be moving in a decidedly different direction.

Just as Pirro’s show was whisked off the air, Democratic National Party Chair Donna Brazile made her debut on the network as a regular contributor and it was announced that former House Speaker Paul Ryan, one of the few red-state reps who dared criticize Trump (however mild that criticism was), is now a board member of the freshly minted company Fox Corp.

That doesn’t mean Rachel Maddow will soon be replacing Sean Hannity, as amusing as that might be. Lachlan and Fox are conservative through and through, but the network may no longer be comfortable serving as the unofficial media arm of the administration. And that could be as much of a business decision as a philosophical one.

A recent protest outside Fox NYC headquarters during an event for advertisers was led by the liberal-leaning watchdog group Media Matters. The brandished signs read “Fox News Is Toxic.” The goal was to get advertisers to take their business elsewhere, as protesters marched in front of story-high images of Fox’s star personalities.

Many of the hosts whose faces are emblazoned on the side of the network’s headquarters have spent two years debunking the Russian collusion witch hunt, special counsel Robert Mueller’s investigation and the entire FBI.

Tensions peaked throughout the media Friday upon news that Mueller’s report had been delivered. The impending biggest story of the year, or replay of Al Capone’s vault, will certainly present challenges inside Fox, where sources have been quoted saying the newsroom wants to put its reporting and journalism front and center.

Hannity and others have breached critical ethical lines between the press and the White House by privately advising the president and even jumping on campaign stages with him.

Pirro’s commentary is at the top of that list. She was suspended after saying Omar was unpatriotic because she wears a hijab, and that means she honors Sharia law over the Constitution. It was as logical an equation as adding two plus two and coming up with 22.

That sort of bad math didn’t appear to rattle Fox before. But less than a week after Pirro’s loaded commentary, 50 Muslims were killed in two New Zealand mosques by a gunman espousing hate for Muslims and others on social media.

Never have TV viewers seen such contrast in Muslim images after New Zealand’s attacks »

Her comments had already triggered widespread criticism, and Fox issued a rare apology.

It was a particularly busy week for Trump, who tweeted that Fox should bring Pirro back, then defended Tucker Carlson, then criticized three of the network’s news anchors, at least one of whom hadn’t apparently been supportive enough of his other tweets attacking the late Sen. John McCain.

The divisions between old school, conservative ideals and reactionary nationalist ideology, and the battle between lifetime career politicians vs. a millionaire heir “populist,” were on full display as he denigrated the late war hero throughout the week.

Appealing to his base’s distrust of the party’s political elite, Trump ripped McCain apart in a series of tweets, and later, sound bites. “He campaigned on repealing and replacing Obamacare for years, and then he got to a vote and he said thumbs down. ... I think that’s disgraceful, plus there are other things.”

McCain’s daughter Meghan said Monday on ABC’s “The View” that Trump spends his weekends “obsessing over great men” because he knows “he will never be a great man.” She also said, “My father was his kryptonite in life. He’s his kryptonite in death.”

Republican lawmakers remained, for the most part, silent as he desecrated their former friend and colleague’s memory. Senate Majority Leader Mitch McConnell avoided locking horns with his leader by releasing a statement highlighting McCain’s attributes. He was “a rare patriot,” he tweeted.

Sen. Lindsey Graham, once a close friend of McCain’s but increasingly a pal of Trump’s, released a statement that belied about as much conviction as a wet sponge. “I think the president’s comments about Sen. McCain hurt him more than they hurt the legacy of Sen. McCain,” Graham said. “My job is to represent the people of South Carolina. They want me to work with the president where I can. I’ve gotten to know the president. We have a good working relationship. I like him. I don’t like it when he says things about my friend John McCain.”

It’s worth noting both McConnell and Graham are up for re-election in 2020. It’s yet to be seen which side of Fox News, or the Republican Party, will be behind them.

lorraine.ali@latimes.com

@lorraineali