The U.S. Supreme Court left intact a Mississippi law that lets businesses and government workers refuse on religious grounds to provide services to gay and transgender people.

The justices turned away two appeals by state residents and organizations that contended the measure violates the Constitution. A federal appeals court said the opponents hadn’t suffered any injury that would let them press their claims in court.

The cases are testing states’ ability to regulate what happens when LGBT rights come into conflict with religious freedoms. Colorado is aiming to bolster gay rights by enforcing an anti-discrimination law, even though the Denver-area baker says he has a religious objection to same-sex marriage.

The measure says religious people can’t be sued or penalized by the government for declining to provide services for same-sex marriage ceremonies. The law also protects people who believe gender is an immutable characteristic or who object to sex out of wedlock.

Critics say the law lets government clerks refuse to issue same-sex marriage licenses and lets adoption and foster-care organizations decline to place children with LGBT families. The measure also wiped out protections that cities including Jackson, the state’s most populous, had previously afforded to gay and transgender residents.

The suing residents and groups contended the statute unlawfully endorses a religious viewpoint and infringes the constitutional right to equal protection.

The cases are Barber v. Bryant, 17-547, and Campaign for Southern Equality v. Bryant, 17-642.