The Supreme Court on Tuesday appeared skeptical of Colorado’s effort to require Catholic preschools to allow parents who do not follow Catholic beliefs to be allowed into its universal preschool program, teeing up a potential fourth major loss for the Centennial State on First Amendment cases at the Supreme Court in the past decade.

The high court heard oral arguments in St. Mary Catholic Parish v. Roy, a case involving the state’s decision to bar Catholic preschools from its universal preschool programs because they refuse to comply with standards requiring schools to admit any child. Colorado defended its decision because it required the Catholic preschools to accept all families, including those who do not share Catholic beliefs, to be part of the state program. The coalition of Catholic schools argued that asking them to admit families who do not follow Catholic teachings would sacrifice their beliefs, which they say violates their First Amendment rights.

A majority of the justices appeared likely to side with the Catholic schools. A main point of contention was the state’s concern that the schools would likely bar the children of same-sex couples, as same-sex marriage goes against Catholic doctrine.