WASHINGTON — A two-page federal form has provoked a titanic clash between the government and many religious organizations.

The form allows some religious organizations to opt out of providing contraceptive coverage, which many insurers and group health plans are required to provide under the Affordable Care Act and related rules.

The opt-out sounds like a way to accommodate religious beliefs. But many religious employers like Wheaton College and the Little Sisters of the Poor are unwilling to sign the form. By signing it, they say, they would authorize their insurers or plan administrators to pay for contraceptives, including some that they believe may cause abortion.

Fights over the form are playing out in dozens of courtrooms around the country. In a separate case, the Supreme Court ruled on June 30 that family-owned for-profit corporations like Hobby Lobby Stores were not required to provide insurance coverage of contraceptives to employees if the companies objected on religious grounds. The Senate planned to take up legislation to reverse that decision this week.