“There’s no dearth of evidence of the disconnect between the president and Republican orthodoxy,” said Mr. Edelman, a longstanding critic of Mr. Trump. But Mr. Edelman noted that the disagreement has been rooted in Congress. “As you look at the Republican Party in the electorate, I think it’s lining up a little more with the president because I think he’s shifting Republican voters more on things like trade and Russia, maybe on Syria and Afghanistan.”

Indeed, many of Mr. Trump’s supporters have cheered his more protectionist stance on trade and the tariff wars with China as well as American allies. Likewise, many Trump supporters have grown weary of overseas military ventures that never seem to end and therefore applaud his moves to bring home American troops. Polls have even detected a shift in Republican views on Russia, which throughout the Cold War was a unifying force in the party.

In Republican circles in Washington, however, the unease coincides with a critical juncture in Mr. Trump’s foreign policy. His pullouts from Syria and Afghanistan come as trade talks with China head toward a climactic deadline and Mr. Trump prepares to get together next month with North Korea’s leader, Kim Jong-un, for their second summit meeting after an initial encounter in Singapore last year.

Olivia Enos, a policy scholar on Asia at the Heritage Foundation, said doubts had grown about Mr. Trump’s negotiations with North Korea to eliminate its nuclear program.

“Many initially welcomed the president’s pursuit of diplomacy in North Korea,” she said. “But after Singapore, many questioned whether North Korea was sincere in coming to the negotiating table. Since that time, North Korea has continued to play hard to get, calling its sincerity to denuclearize into further question.”

Some analysts said it was the way Mr. Trump makes his decisions as much as the decisions themselves that rattle the foreign policy establishment. Announcing the Syria pullout by Twitter without preparing the allies or framing the public explanations left even some of the president’s strongest supporters in Washington unnerved.

“I don’t think Leader McConnell or anyone else wants to take the wheel from the president or even give him rudder direction,” said Frederic C. Hof, a former State Department official who worked on Syria and is now diplomat in residence at Bard College. “They want to be sure he’s at the helm and he knows he has a crew. They want real deliberation to take place on these tough issues. They want the president to be part of it.”