Washington (CNN) Donald Trump has pointed to his hiring chops as a key asset, but he is already facing calls to rescind a job offer to one of his top national security picks.

Ret. Gen. Michael Flynn, the 57-year-old former head of the Defense Intelligence Agency, has been selected as the next US national security adviser.

He has also spread false stories and re-tweeted anti-Semitic threats. He's been criticized for dabbling in conspiracy theories and Islamophobia, for his questionable ties to foreign governments and for mishandling classified information while at the DIA, a post he was pushed out of.

On Monday, 53 non-profit groups appealed to Trump to reconsider the appointment, as lawmakers publicly questioned Flynn's judgment and demanded that he disavow fabricated conspiracy theories such as the "Pizzagate" story -- which his son Michael Flynn Jr. promoted -- alleging that Democrats ran a child sex ring out of a Washington pizza restaurant.

"It is incumbent on Trump, his nominee for National Security Advisor, General Flynn, and his entire team to disavow these falsehoods and conspiracy theories," the top Democrat on the House Permanent Select Committee on Intelligence, Adam Schiff, said in a statement. "They will soon have a country to run, and God help us if they conduct the nation's affairs like their transition -- without the willingness or ability to separate fact from fiction."

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The NSA job doesn't require congressional approval, unlike Cabinet posts.

The non-profit groups, a mix of religious and social justice organizations, said they respected Flynn's 33 years in uniform, but claimed that his appointment would damage US standing in the world and pose a threat to national security.

"General Flynn's appointment as National Security Advisor is a frightening prospect for anyone who values America's national security and ability to promote stability and prosperity around the globe," the group wrote. "We call on you to rescind it immediately."

Flynn's inflammatory comments have drawn public scrutiny, and now the spotlight is widening to include his son, who also has a history of spreading fake news and conspiracy theories. The younger Flynn's online activities came under fire most recently after an armed man who believed the Pizzagate rumors entered the Washington restaurant and fired shots.

Flynn's son becomes a lightning rod for criticism

The younger Flynn insisted afterward on Twitter that rumors about the pedophilia ring were true until they could be disproved.

The restaurant, whose patrons are puzzled by the rumors and aghast that a beloved neighborhood institution has been targeted, has unequivocally denied the stories.

Flynn's son had been on the transition team doing scheduling work for his father, according to Trump spokesman Jason Miller. He has since left the team, though Trump officials wouldn't explain why.

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Government sources told CNN's Jake Tapper that a security clearance had been requested for the younger Flynn.

Vice President-elect Mike Pence wouldn't answer Tapper's repeated questions on "The Lead" Tuesday about whether he knew the transition team sought the security clearance. Instead, Pence said the younger Flynn had merely been helping his father with scheduling and administrative matters.

The son's tweets fit into a pattern of spreading false and inflammatory stories that his father has already established, critics have charged. In their letter, the non-profit groups decry what they called Flynn's "history of bigoted and deceitful statements," particularly with reference to Islam.

Flynn has tweeted that "fear of Muslims is rational" and made no distinction between ordinary Muslims and radical Islamic terrorists. "This is Islamism and it is a vicious cancer inside the body of 1.7 billion people on this planet and it has to be excised," he said in one speech.

He's also retweeted anti-Semitic comments . After Hillary Clinton's campaign said that Russia was behind a hack of the Democratic National Committee -- an assessment reached by the US Intelligence Community -- and had done it to help Trump's campaign, Flynn erupted on Twitter.

"The corrupt Democratic machine will do and say anything" to get Clinton into the White House, Flynn wrote as he retweeted a Twitter account that made reference to Judas.

" 'The USSR is to blame!' " the tweet read. "Not anymore, Jews. Not anymore."

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And more than once he has been tagged in his tweets an anti-Semitic commentator named Jared Wyland, who has tweeted about the "liberal Jewish Media."

Sen. John McCain lends his support

Some key Republicans, however, are signaling their support for the controversial retired general.

Arizona Sen. John McCain, the Republican who heads the Senate Armed Services Committee, was asked by CNN's Dana Bash whether he had concerns that a future national security advisor would, among other things, spread false news stories. "I feel comfortable," McCain said.

The retired three-star general ran intelligence for the US Joint Special Operations Command, which includes SEAL Team 6 and Delta Force, before moving on to command the Defense Intelligence Agency, the US military's overall intelligence organization.

Flynn was fired by the Obama administration after two years as the head of DIA. Four US officials serving at the time told CNN it was because of his contentious management style.

On at least two occasions, his handling of classified information came under scrutiny, leading to informal reprimands but no charges of wrongdoing, according to reporting by CNN's Barbara Starr.

Questions about foreign ties

Flynn attributed his dismissal to White House anger that he insisted on identifying radical Islamic terrorism as the greatest threat facing the US.

In retirement, Flynn began advising Republican candidates, eventually speaking at the Republican National Convention, where he led the crowd in chants against Clinton, shouting, "Lock her up!" from the stage.

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Flynn's ties to foreigners and other governments have also raised concerns.

Lobbying disclosure documents filed in September revealed that even as Flynn was received classified intelligence briefings during the campaign, he was lobbying on behalf of overseas clients.

The Flynn Intel Group, which advertises itself as "all source intelligence support to global challenges," was working for a Turkish-American businessman with ties to Turkey's president, even as he was getting the sensitive briefings. Flynn has defended Turkey's crackdown on dissent

and advocated that the US extradite a Pennsylvania resident who President Recep Tayyip Erdogan accuses of staging a July coup attempt.

Flynn said he would sever his ties to the business if he became a formal member of the Trump administration.

Flynn also had financial ties to Russia, in the form of a paid speaking gig with Russia Today , a TV network founded by the Kremlin. In sharp contrast to current military leaders who see Russia as a geopolitical threat, Flynn wants to build closer cooperation with Russia even as the country has annexed Crimea and supported the Syrian regime.

Schiff said that "the incoming President would be better served by someone with a healthy skepticism about Russian intentions, and willing to be guided by the unequivocal intelligence we have of Russian's malignant policies towards the U.S. and our allies."