When 12,000 public health professionals gathered in Minneapolis last week for the annual meeting of the American Public Health Association, Dr. Jerome Adams, who served as surgeon general in the first administration of President-elect Donald J. Trump, issued a pointed warning about Robert F. Kennedy Jr.

“If R.F.K. has a significant influence on the next administration, that could further erode people’s willingness to get up to date with recommended vaccines,” Dr. Adams said. “I am worried about the impact that could have on our nation’s health, on our nation’s economy, on our global security.”

Now, Mr. Kennedy, a vocal skeptic of vaccines, is in a position to have significant influence, and over a broad range of policy. Mr. Trump’s sweeping electoral victory, with Mr. Kennedy at his side, is — in the eyes of their supporters — not only a mandate but also a repudiation of the public health establishment that has long kept Mr. Kennedy at bay.

As an independent presidential candidate and as a surrogate for Mr. Trump, Mr. Kennedy pledged to upend the nation’s agriculture system and public health bureaucracy, effectively gutting whole swaths of the regulatory state, under the rubric of rooting out “cronyism” and corruption.

After Mr. Trump was first elected in 2016, Mr. Kennedy told reporters that Mr. Trump promised to let him chair a vaccine commission, but it never came to pass. Now, Mr. Kennedy has a much stronger hand, having rallied his followers behind Mr. Trump. The president-elect has indicated that Mr. Kennedy will play a role in his new administration and recently said he would let Mr. Kennedy “go wild on health,” but he has not been specific about what that means.

Some have speculated that Mr. Trump will make him a “health czar” inside the White House, to guide the president on public health matters; a person familiar with the transition said Mr. Kennedy was at Mar-a-Lago on Wednesday and spoke with Trump insiders about the public health agenda.