Now it’s being called out by Robert F. Kennedy, Jr. —possibly on track to become head of health initiatives for the incoming presidential administration—as a practice that should be halted. He recently asserted that Donald Trump would push to remove fluoride from drinking water on his first day in office.

Mr. Kennedy, an environmental lawyer who has no medical or public health degrees, has promoted anti-vaccine conspiracies for years.

Trump's victory gives a broader platform to critics of federal health programs. Among other moves, he may try to weaken the Affordable Care Act and cut funding for Medicaid coverage.