WASHINGTON — The Supreme Court on Wednesday seemed ready to take another step in requiring states to pay for religious education, with a majority of the justices indicating that they would not allow Maine to exclude religious schools from a state tuition program.

The court has said that states may choose to provide aid to religious schools along with other private schools. The question in the new case was the opposite: Can states refuse to provide such aid if it is made available to other private schools?

Maine requires rural communities without public secondary schools to arrange for their young residents’ educations in one of two ways. They can sign contracts with nearby public schools, or they can pay tuition at a private school chosen by parents so long as it is, in the words of state law, “a nonsectarian school in accordance with the First Amendment of the United States Constitution.”

Two families in Maine that send or want to send their children to religious schools challenged the law, saying it violated their right to freely exercise their faith.

Religious people and groups have been on a winning streak at the Supreme Court, which seemed likely to continue in the new case. In recent decisions, the justices have ruled against restrictions on attendance at religious gatherings to address the coronavirus pandemic and Philadelphia’s attempt to bar a Catholic agency that refused to work with same-sex couples from screening potential foster parents.

The court also ruled that the Trump administration could allow employers with religious objections to deny contraception coverage to female workers and that employment discrimination laws do not apply to many teachers at religious schools.

The point of Maine’s law, said Christopher C. Taub, a lawyer for the state, was to provide something resembling a public school education to young people in remote areas. “That is the benefit at issue here: a free public education,” he said. “That private schools are sometimes enlisted to deliver the benefit is of no constitutional significance.”

Justice Elena Kagan said Maine’s program sought to solve a distinct problem.

“This is really a default program for a very small number of students living in isolated areas where the state has decided it does not have the resources to provide public schools,” she said.

Justice Samuel A. Alito Jr. asked whether the program allowed parents to use state money for tuition at elite private boarding schools in other states but not at local religious ones.

Mr. Taub said yes. “An Andover or a Phillips Exeter may be different from Bangor Public High School in many different ways,” he said. “But what they share in common is the most important feature, which is that they are not inculcating religion.”

The case, Carson v. Makin, No. 20-1088, was broadly similar to one from Montana decided by the court last year. In that case, the court ruled that states must allow religious schools to participate in programs that provide scholarships to students attending private schools.

Chief Justice John G. Roberts Jr., writing for the majority in that case, Espinoza v. Montana Department of Revenue, said a provision of the state's Constitution banning aid to schools run by churches ran afoul of the federal Constitution’s protection of the free exercise of religion by discriminating against religious people and schools.

“A state need not subsidize private education,” he wrote. “But once a state decides to do so, it cannot disqualify some private schools solely because they are religious.”

But the Montana decision turned on the schools’ religious status rather than their curriculums. There might be a difference, Chief Justice Roberts wrote last year, between an institution’s religious identity and its conduct.

“We acknowledge the point,” he wrote, “but need not examine it here.” The Maine case will turn on the point.

Chief Justice Roberts and other conservative justices made clear on Wednesday that they thought the distinction drawn in the Montana case, between religious status and religious activity, made no constitutional difference.

The chief justice asked, for instance, whether the state would pay for tuition at a religious school whose doctrine calls for public service and that “does look just like a public school, but it’s owned by religion.” Mr. Taub said yes.

What about a religious school that “is infused in every subject with their view of the faith?” the chief justice asked. Mr. Taub said such a school would not qualify.

Chief Justice Roberts said that was an important concession. “So you’re discriminating among religions based on their belief, right?” he asked, adding that the government may not “draw distinctions between religions based on their doctrine.”

Michael Bindas, a lawyer with the Institute for Justice, a libertarian group that represents the families, said that “religious discrimination is religious discrimination.”

“Religious schools, after all, teach religion, just as a soccer team plays soccer or a book club reads books,” he said. “Yes, it is part of what they do. It is also part of who they are.”

One of the schools at issue in the case, Temple Academy in Waterville, Maine, says it expects its teachers “to integrate biblical principles with their teaching in every subject” and teaches students “to spread the word of Christianity.” The other, Bangor Christian School, says it seeks to develop “within each student a Christian worldview and Christian philosophy of life.”

The two schools “candidly admit that they discriminate against homosexuals, individuals who are transgender and non-Christians,” Maine’s Supreme Court brief said.

Justice Elena Kagan said that point was not in dispute. “These schools are overtly discriminatory,” she said. “They’re proudly discriminatory. Other people won’t understand why in the world their taxpayer dollars are going to discriminatory schools.”

Justice Neil M. Gorsuch said that Maine’s anti-discrimination laws were not at issue in the case.

Much of the argument was devoted to hypothetical questions. Mr. Taub volunteered that schools that taught Marxism, Leninism or white supremacy “would be doing something completely inconsistent with a public education,” though he conceded that the state law at issue in the case does not currently forbid that.

“Would you say the same thing about a school that teaches critical race theory?” Justice Alito asked.

Mr. Taub said that he did not “know exactly what it means to teach critical race theory” and that “the Maine Legislature would have to look at what that actually means.”