WASHINGTON — In his West Wing office, Stephen K. Bannon kept a chart listing trade actions — on China, steel and autos — that the Trump White House planned to roll out, week by week, through the fall. Now that Mr. Bannon, the president’s chief strategist, has been pushed out, the question is whether his agenda will be erased along with him.

It is not just trade: Mr. Bannon has had a strong voice on issues from climate change and China to immigration and the war in Afghanistan. He has been an unyielding advocate for a visceral brand of nationalism, and though he lost as often as he won in policy debates, his departure could tip the balance on some fiercely contested issues toward a more mainstream approach, even if the core tenets of his philosophy survive.

Mr. Bannon’s dorm-like office functioned as a sort of command center for the administration’s nationalist wing. He met there with a coterie of mostly young, like-minded colleagues, planning strategy and plotting against foes, from Lt. Gen. H.R. McMaster, the national security adviser, to Gary D. Cohn, the director of the National Economic Council.

Some of Mr. Bannon’s protégés have already been sidelined while others may depart soon, people in the White House said. He will no longer have access to briefing papers or sit in meetings, like a regular Tuesday morning session in the Roosevelt Room where he sparred with Mr. Cohn and other officials over the timing of trade moves against China.