Still, Trump’s address from the White House on Monday, full as it was with errors and overstatements, is causing headaches for his advisers. They are uneasy with Trump’s willingness to raise women’s alarm when the evidence is mixed about the risk of taking Tylenol, and virtually nonexistent with regard to vaccines, two of the people told POLITICO. Inside the administration, the people said health officials have had to make peace with the president’s view that it’s better for women to be needlessly cautious than to risk harming their babies.

The reaction to Trump’s speech among public health advocates was overwhelmingly negative. In statement after statement, doctors’ groups, experts and scientists said Trump’s warnings weren’t backed by the science and would prompt many women not to treat pain and fevers or vaccinate their children, putting them at risk of disease. The rising rates of autism, many public health experts believe, are partly the result of changing diagnostic criteria and more awareness of the condition. They also suspect a variety of environmental and genetic factors could be involved.

The critics have no credibility with Trump, the people close to the White House said. Trump, like his health secretary, Robert F. Kennedy Jr., blames them for standing by while autism rates grew.

“That’s the establishment. They’re funded by lots of different groups,” Trump said Monday in response to a reporter’s question on the president’s reaction to a doctor’s group stating Tylenol was a sa