WASHINGTON — Two dozen Democratic-led states, counties, and cities sued on Tuesday to overturn a new Trump administration rule that would protect health care workers who refuse medical procedures — like abortion, assisted suicide, or sex reassignment surgery — if it violates their “conscience.”

An 80-page complaint in federal court in Manhattan argues the policy could have dire effects for patients, particularly low-income people of color, women, and LGBT people who disproportionately rely on government-backed health care systems.

The Department of Health and Human Services’ final rule is scheduled to take effect in July, and if implemented it would cut off federal funds to institutions that prevent health care workers from recusing themselves on religious grounds.

The plaintiffs allege this is an attempt at coercion, overstepping the federal government's authority and saying the “financial exposure could amount to hundreds of billions of dollars each year” for governments that use federal funding for their health care systems.

Workers could opt out of performing services without any advance warning to their employers, which would be banned from asking employees about religious objections in advance, the lawsuit says. They argue this undermines their own government-run health care systems, which include hospitals and health care agencies, by conflicting with local policies that ban discrimination.

“This change to put providers above patients comes at a dangerous price,” says the complaint in New York.

For example, court documents say, “If a woman arrives at the emergency room of one of Plaintiffs’ institutions presenting with a ruptured ectopic pregnancy, the Final Rule would permit a wide swath of employees — from receptionists to nurses to doctors to pharmacists to anesthesiologists — to refuse to assist that patient in real time, and without any advance notice, no matter the intense medical risk to the patient.”

They also contend employers could not ask if a job applicant for a nursing position “had a religious objection to administering a measles vaccination, regardless of whether such a duty was a core element of the position needed during an outbreak of the disease.”