A sharply divided Supreme Court ruled Tuesday that Montana can create a tax credit program for private tuition assistance even though it would mean most money goes to religiously affiliated schools, allowing states to set up such programs even if their state constitution bans aid for churches and religious schools.

The 5-4 decision reversed a Montana Supreme Court ruling that had eliminated the entire state program based on a “no-aid” provision in the state’s constitution, which prohibits any aid to a school controlled by a “church, sect, or denomination.”

Chief Justice John G. Roberts Jr. and the four other members of the court’s conservative wing decided that ruling violated the Free Exercise Clause of the Constitution — the latest case to reshape the line where tax money can flow to religiously affiliated organizations.

The majority found the Montana “no-aid” provision as applied to this program unconstitutionally bars religious schools, and parents who wish to send their children to those schools, from public benefits solely because of the religious character.

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

That is the first time the court ordered such a requirement, legal experts said.

The Catholic Association called the decision a welcome victory for state constitutional amendments that have anti-Catholic roots and have been known to discriminate against religions. Public school backers said it would divert funding from already financially struggling schools.

“At a time when public schools nationwide already are grappling with protecting and providing for students despite a pandemic and mounting budget shortfalls, the court has made things even worse opening the door for further attacks on state decisions not to fund religious schools,” National Education Association President Lily Eskelsen García said in a news release.

The case was brought by three mothers whose children attend Stillwater Christian School in northwestern Montana. Their lawyers argued that 20 of 37 states with no-aid provisions allow religious options in publicly funded scholarship programs, and almost all allow religious options in tax credit programs, the majority opinion points out.

Many parents exercise their right to direct the religious upbringing of their children by sending them to religious schools, “a choice protected by the Constitution,” Roberts wrote. “But the no-aid provision penalizes that decision by cutting families off from otherwise available benefits if they choose a religious private school rather than a secular one, and for no other reason.”

The four justices of the court’s liberal wing dissented. Justice Ruth Bader Ginsburg wrote that the Supreme Court should not have addressed the controversy because the Montana Supreme Court did not disqualify private schools because they were religious — it struck down the whole program.

Rather than discriminate, that “put all private school parents in the same boat,” Ginsburg wrote in the dissent joined by Justice Elena Kagan.

And Justice Stephen G. Breyer, in a dissent joined by Justice Sonia Sotomayor, argued that the Establishment Clause does not forbid Montana’s program, but it does not require Montana to do so as the majority ruled.

In 2015, the Montana legislature enacted a bill that provided two types of dollar-for-dollar tax credits to taxpayers who donate to either public schools or the Tax Credit Program, up to $150.