WASHINGTON — The Supreme Court on Monday took up its latest case asserting religious rights claims, agreeing to hear arguments that Colorado should exempt Catholic entities from a nondiscrimination provision in its state-funded preschool program.

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The Archdiocese of Denver, which runs 34 preschools, says it is excluded from the statewide program because of a nondiscrimination rule that prohibits preschools from refusing admission to any child on the basis of sexual orientation and gender identity.

The archdiocese says this conflicts with its religious rights under the Constitution’s First Amendment because Catholic religious doctrine does not recognize same-sex relationships or transgender status.

Also involved in the case are two Catholic parishes in Littleton and Lakewood, and two parishioners, Daniel and Lisa Sheley. The Sheleys have five children, two of whom are currently in preschool.

The Trump administration filed a brief in support of the archdiocese urging the court to take up the case.

The preschool program, approved as part of a statewide referendum in 2020, provides taxpayer funds for parents to send their children to their preferred preschool.

At the center of the archdiocese’s argument is the scope of a 1990 Supreme Court ruling called Employment Division v. Smith, which stated that religious exemptions are not required when a law applies equally to everyone.

The archdiocese’s lawyers say the Catholic entities should get an exemption in this instance because the law and related regulations are already riddled with loopholes that give preschools leeway when weighing applications. (Schools, for example, can prioritize children with disabilities and those from low-income families.) Therefore, the law does not apply equally under the Supreme Court ruling, they say.

The state counters that the focus should only be on the nondiscrimination provision itself, which has no exemptions, meaning that under Supreme Court precedent, the Catholic preschools are not owed a carveout.

The archdiocese sued in 2023 but lost in federal district court and the Denver-based 10th U.S. Circuit Court of Appeals.

The Supreme Court has a 6-3 conservative majority that often backs religious rights claims. In recent years, it issued a series of rulings that rolled back limits on religious entities participating in government programs, including those related to education.