Critics point to Bannon's leadership at the "alt-right" Breitbart News website in painting him as racist and anti-Semitic. Trump's advisers, though, praise Bannon's ability to keep Trump on message as an asset for the transition and the presidency.
"The guy I know is a guy that isn't any of those things," Priebus said, describing his close work with Bannon during the general election. "In the last few months, he's exhibited none of those qualities."
"If Trump is serious about seeking unity, the first thing he should do is rescind his appointment of Steve Bannon," said Reid, who is retiring in January. "Rescind it. Don't do it. Think about this. Don't do it."
Most of the criticism stems from Bannon's affiliation with Breitbart News.
In July, Bannon told Mother Jones that Breitbart was "the platform for the alt-right."
The alt-right emerged as a counterpoint to mainstream conservatism, though some leaders and followers of the movement have come under fire for espousing racist views.
The Southern Poverty Law Center said in a statement Monday, "The alt-right, as we know, is simply a rebranding of white nationalism and is the energy behind the avalanche of racist and anti-Semitic harassment that plagued social media platforms for the entire presidential campaign. Once the news of Bannon's appointment hit white supremacist websites last night, forums like Stormfront erupted in celebration."
In 2014, Bannon told the Daily Beast, "I'm a Leninist. Lenin wanted to destroy the state, and that's my goal, too. I want to bring everything crashing down, and destroy all of today's establishment."
Nationally syndicated radio host Glenn Beck, a controversial conservative, calls the alt-right movement "truly terrifying," telling CNN's Anderson Cooper that Bannon "has given a voice and power to that group of people."
"You don't empower people like that. You just don't. It's not smart," he said.
"All of this is to scare the living daylights out of you," said Hannity, who also hosts a show on Fox News. "All of this is to create an impression, just like during the election. The attempts now to disenfranchise the Trump agenda has begun. The radical left will be on display, just like during the Bush years."
Bannon's appointment has drawn praise form the Ku Klux Klan, neo-Nazis and other white nationalist groups.
Bannon was born on Nov. 27, 1953, in Norfolk, Va., to a working-class family of Irish Catholic, pro-Kennedy, pro-union Democrats.
Now 62, he holds an MBA from Harvard University and a master's degree in National Security Studies from Georgetown University. He's a Navy veteran who has worked at Goldman Sachs and was an early investor in the TV show Seinfeld. He is the father of adult twins, divorced from their mother.
Bannon was appointed executive chairman of Breitbart News in 2012 after the death of its founder, Andrew Breitbart. He was already a member of the board.
Breitbart News Senior Editor-at-Large Joel B. Pollak said Wednesday on National Public Radio that Bannon is a "a fantastic choice" for Trump and "from a conservative perspective at least, a national hero."
"Steve Bannon is a fantastic manager," said Pollak, who is an Orthodox Jew. "He helped Breitbart grow fantastically, to the point where we have 250 million page views per month. He is a leader with vision, he's very disciplined, he insists on excellence from those around him. He's also very open to debate and challenge as long as you bring facts and data to the table. And he has no prejudices. He treats people equally, and in fact during my time working closely with him at Breitbart for five years, he sought out people from diverse backgrounds, and gave them a voice at Breitbart."