Donald Trump's chief strategist and former campaign chief Steve Bannon, who has been accused of holding radical views, has been appointed to the U.S. National Security Council.

Bannon and Stephen Miller were the driving force behind some of the directives in Trump's recent executive order on limiting Syrian refugees and prohibiting immigration from seven Muslim countries, including the one on green card holders entering the U.S., according to CNN, who cited a Republican close to the White House.

The hashtag #StopPresidentBannon hit the top of Twitter's U.S. trending chart as Twitter users began en masse to protest President Trump's chief strategist's new found influence.

Many of the memes circulating Twitter invoke Bannon's now infamous self-description as a "Leninst." "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," Bannon had told a writer for the Daily Beast in 2013.

U.S. Senator John McCain said on Sunday that Trump's order targeting immigration from seven predominantly Muslim countries has been "confusing" and raised a number of questions.

McCain said he was "worried" about the addition of Trump's chief strategist to the U.S. National Security Council. McCain said this was "a radical departure from any national security council in history."

"It's been a very confusing process," McCain, a Republican and chairman of the Senate Armed Services Committee, told CBS' 'Face the Nation.' McCain said the effect of Trump's immigration order "will probably, in some areas, give ISIS (Islamic State) some more propaganda," and asked why the countries targeted by the order included Iraq, where U.S. forces are fighting alongside Iraqi forces against Islamic State.

Green cards?

The Trump administration official later told reporters that U.S. green card holders traveling outside the United States need to check with a U.S. consulate to see whether they can return.

"It's being cleared on a case-by-case basis," the official said.

On Sunday morning, the administration addressed the issue again but left questions over how green cards holders would be screened and by what agencies.

"The executive order doesn't affect green card holders moving forward," White House Chief of Staff Reince Priebus addressed told NBC's "Meet the Press." He added that they would be subjected to extra questioning by CBP agents when they tried to re-enter the United States.

A senior administration official told Reuters, however, that it had not been determined where and how those screenings would be carried out. The nature of the screening will be up to CBP or the State Department, the official said, and specific guidelines were being drafted.

"They could be screened in many different ways and in many different places," the official said in an interview.