(Pablo Martinez Monsivais/AP)

The Supreme Court agreed Friday to hear another challenge to the Affordable Care Act, this time to decide whether religiously affiliated organizations such as universities, hospitals and charities can be free from playing any role in providing their employees with contraceptive coverage.

The case pits questions of religious liberty against a woman’s right to equal health-care access, and it will be the fourth time the court has considered some aspect of what has come to be known as Obamacare.

The Obama administration says it has provided the organizations with an easy way to opt out of the legal requirement that employers include contraceptives as part of health insurance coverage. Employers who object must make clear their religious objections and let insurance companies and the government take over from there.

But the groups say even that step would implicate them in what they believe to be a sin, adding that they face ruinous fines if they refuse to comply. They want to be included under the blanket exemption from providing the coverage that the government has extended to churches and solely religious groups.

The court accepted seven cases from throughout the country, including one challenge involving the Roman Catholic Archdiocese of Washington and another from an order called the Little Sisters of the Poor, which runs homes for the aged.

Conflicting lower-court decisions resulted in supporters and opponents of the law calling for the Supreme Court to act.

White House press secretary Josh Earnest noted that seven appeals courts had sided with the government’s position, and he said the administration is confident that “the policy we have in place appropriately balances the need of millions of Americans to have access to birth control, while also protecting the right of religious freedom that is protected in the Constitution.”

Mark Rienzi, senior counsel for the Becket Fund for Religious Liberty, which represents the nuns, said government should not be “allowed to say that the Sisters aren’t ‘religious enough’ to merit the exemption that churches and other religious ministries have received.”

The cases are something of a sequel to the court’s narrow decision in 2014’s Burwell v. Hobby Lobby that some closely held corporations are protected from having to provide contraceptive coverage that offends the owners’ religious beliefs.

The owners claimed that the contraceptive mandate being carried out by the Department of Health and Human Services violates the Religious Freedom Restoration Act (RFRA).

The RFRA says the government must have a compelling reason for laws and programs that substantially burden religious beliefs, and even then government must prove that the law is the least burdensome way of achieving its goal.

In ruling for Hobby Lobby, the court’s conservatives suggested that one reason the business owners in that case had a valid complaint was that the government had made special arrangements for churches and religious nonprofits but not for them.

In the current litigation, most appeals courts have dismissed the religious nonprofits’ complaints because the government has offered them the work-around that the Supreme Court seemed to require in the earlier case.

“All plaintiffs must do to opt out is express what they believe and seek what they want via a letter or two­-page form,” Judge Cornelia Pillard said when the case involving the Washington archdiocese came before the U.S. Court of Appeals for the D.C. Circuit. “Religious nonprofits that opt out are excused from playing any role in the provision of contraception services, and they remain free to condemn contraception in the clearest terms,” she wrote.

But several prominent conservative judges have protested the rulings, and in September, the U.S. Court of Appeals for the 8th Circuit, in St. Louis, ruled against the government.

In a case involving a college and a religious charitable organization, Judge Roger Wollman wrote for a unanimous appellate panel that the issue is whether the groups “have a sincere religious belief that their participation in the accommodation process makes them morally and spiritually complicit in providing abortifacient coverage. Their affirmative answer to that question is not for us to dispute.”

Wollman said it was clear that the fines imposed for failing to comply with the mandate would be a substantial burden on the groups and that the government did not meet the test of proving there was no other way to meet its goal of providing women with contraceptive coverage.

The government says the rules should be different for churches than for the organizations in the current fight. Churches and purely religious organizations are more likely to hire workers who share their religious beliefs. Universities, hospitals and charities, on the other hand, will have many students and employees who do not share the views of the sponsoring religious groups, Solicitor General Donald B. Verrilli Jr. said in the government’s petition to the court.

The issue for the court is whether the religious-freedom law “entitles petitioners not only to opt out of providing contraceptive coverage themselves but also to prevent the government from arranging for third parties to provide separate coverage to the affected women,” Verrilli wrote.

Noel Francisco, representing the archdiocese, countered that the case was about “whether the government can commandeer petitioners and their health plans as vehicles for delivering abortifacient and contraceptive coverage in violation of their religion. . . . Petitioners ask only that they not be forced to participate in this effort.”

To be eligible for the government’s accommodation, a religious organization must certify to its insurance company that it opposes coverage for contraceptives, or it must send a letter to the government saying so and provide the name of its insurance company. The insurers and government take over from there to provide the services.

But the religious groups say either of those options serves as a “trigger” that allows the contraceptives to be provided and makes the groups complicit.

The cases accepted are: Zubik v. Burwell; Priests for Life v. Department of HHS; Roman Catholic Archbiship v. Burwell; Texas Baptist University v. Burwell; Little Sisters of the Poor v. Burwell; Southern Nazarene University v. Burwell; and Geneva College v. Burwell.

The court consolidated the cases, and they will probably be collectively referred to as Zubik v. Burwell. Zubik is the bishop of the Catholic Diocese of Pittsburgh; Sylvia Mathews Burwell is the HHS secretary.

The court sent a letter to attorneys in the case asking them to work out the details of briefing the case and requested that they “keep the number of briefs to a minimum and avoid repetition of argument.”