December 04, 2018 11:35 AM

Despite their often opposing viewpoints, Meghan McCain and Joy Behar have a healthy working relationship.

In the wake of The View co-hosts’ tense on-air exchange during a George H.W. Bush tribute on Monday, a source tells PEOPLE they “are totally fine.”

“They had a disagreement on-air, which is totally expected in that job,” the source says. “But they are both professionals. They seemed completely fine afterwards.”

In fact, according to the source, the two have “actually gotten really close over the last year.” (McCain — daughter of the late Senator John McCain — joined the ABC panel as a permanent co-host in October 2017.)

“They’re two very different people, but they’re both very professional,” the source adds.

Democrat Behar, 76, and Republican McCain, 34, sparred when their discussion about the late president, who died Friday at the age of 94, turned political.

After praising Bush’s environmental efforts while in office, Behar tore into President Donald Trump.

“This president that we have now is trying to unravel everything that he did and [President] Obama did,” she said. “And if I ever become a one-issue voter, it will be about pollution and the greenhouse effect,” she said.

McCain asked that the conversation be redirected back to honoring Bush.

“Can we focus on the president, please?” she said. “I don’t want to talk about Trump when we’re in the moment of honoring a great president who passed. I’m not interested in your one-issue voter when our president just passed.”

“I don’t care what you’re interested in. I’m talking! Damn it,” Behar fired back.

“Well, I don’t care what you’re interested in either, Joy!” McCain said as Whoopi Goldberg instructed the cameras to turn to commercial break.

RELATED VIDEO: In Memoriam: George H.W. Bush

In February, McCain addressed rumors that she was feuding with Behar behind closed doors while appearing on Watch What Happens Live with Andy Cohen

“The idea that we’re fighting backstage? Quite frankly, nobody has time to continue the fight afterwards,” she said.

“The only time I wish I were a man is when you’re a woman on a panel show,” she continued. “Because men are allowed to fight and debate and get really heated and angry and there’s an assumption that they’re friends and they’re smoking cigars and whatever. I’m there to debate and to fight. It’s the point of the show, that we will have difference of opinion — it’s called the frickin’ View.

That said, as a conservative on a liberal-leaning panel in today’s political climate, McCain said it can be hard to get her point across.

“It’s such a difficult job on so many different levels. It’s highly political, it’s highly nuanced,” she said. “Trump’s America makes everything really polarizing, and it’s hard to sort of explain the conservative point of view with some of the topics everyday. But it’s a pleasure and it’s a challenge.”

At the time, a source told PEOPLE that McCain and Behar “fundamentally disagree on everything — on the show.”

“But that’s what they are paid to do,” the source continued. “They have different politics and different views and their job is to argue about this stuff on-air. But the idea that there’s fighting behind the scenes because of it is not true.”

The View airs weekdays (11 a.m. ET) on ABC.

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