The Supreme Court heard arguments on the firing of two teachers at Catholic schools in Los Angeles. (Pablo Martinez Monsivais / Associated Press)

The Supreme Court justices sounded split Monday on whether to broadly deny civil rights protections to hundreds of thousands of teachers in religious schools, as they heard cases involving two who were fired from Catholic schools in Los Angeles.

At issue is whether the Constitution’s protections for religious freedom shields church schools from being sued if they discriminate against a teacher in violation of federal or state laws that protect workers.

Advocates for the teachers warned the justices that a broad ruling based on the church’s view of its religion mission could severely restrict the rights of millions of other employees in church-run hospitals, nursing