The specific question that the Supreme Court discussed Wednesday morning may have been settled before the justices even heard the case.

The matter concerns a Lutheran church in Missouri which applied for state funding to refurbish its preschool playground, but was told that the state Constitution forbids financially supporting a religious institution. The question of whether the church should be eligible for the playground funding made it all the way to the highest court in the nation — but then last week, Missouri’s new governor declared that he was changing the policy, and the church could apply for the playground program after all.

Case closed, right?

Not for the Supreme Court, which heard arguments in Trinity Lutheran Church v. Comer on Wednesday despite the late-breaking news from Missouri. And not for advocates on both sides, who see potentially monumental consequences of the case, either for expanding churches’ access to government funds or for cutting them off from basic government services they have long enjoyed.

 Trinity Lutheran is “one of the most important religious liberty cases before the Supreme Court in years,” said Penny Nance, president of Concerned Women for America, who headed a rally outside the Supreme Court on Wednesday.

“A loss here at the Supreme Court could mean that religious nonprofits could be excluded from government programs meant to serve the community. This is like telling the fire department they couldn’t put out a fire because it’s at a church,” Nance told the crowd at the rally.

Many speakers at the demonstration — as well as Supreme Court Justice Stephen G. Breyer — raised the same fire department question, wondering why a prohibition on the government cutting a check to a church would not also mean a prohibition on basic safety services.

That’s the sort of dire outcome that Christian activists see as a possibility if the preschool loses the Supreme Court case. If the preschool wins, they also foresee consequences far beyond a playground grant.

“This will mean good things for the school choice movement in our country,” said Hillary Byrnes, assistant general counsel of the U.S. Conference of Catholic Bishops. Several organizations of Christian schools at the rally hoped for a broad Supreme Court decision, striking down Missouri’s ban on state funding for religious institutions — a ban similar to policies in more than 30 other states. That would increase the likelihood of states granting funding for school vouchers that children could use at religious primary and secondary schools, they say.

Betsy DeVos, the recently appointed secretary of education, favors expanding school voucher programs across the country.

Nance, a proponent of school vouchers, said that bolstering the legal case for sending public education dollars to church-run schools might be one of the most important outcomes of the Trinity Lutheran case. “I don’t think this one decision’s going to be the magic wand that’s going to make all my dreams come true. I think it does pave the way,” she said in an interview. “This sets precedent. It makes it easier.”

Ralph Reed, chairman of the Faith and Freedom Coalition, pointed out other instances in which it is legal for taxpayer money to go to religious schools — such as a student who goes to Notre Dame or Yeshiva University using G.I. Bill funding, or who pays tuition at Liberty University using a Pell Grant.

The case could be significant for furthering school vouchers, he said in an interview, but “the implications go way beyond that.” He said the court’s decision might clarify the government’s relationship with church-run hospitals, homeless shelters and charities, either opening them up to easier access to federal funds or cutting off money they receive.

The small group of a few dozen Christian demonstrators emphasized the playground theme: They set up a plastic slide and seesaw, blasted an odd mix of Disney music including “A Dream Is a Wish Your Heart Makes” and “Cruella de Vil,” and brought their young children, who played quietly in front of the podium throughout more than an hour of speeches about the case.

There were no demonstrators to be seen advocating for maximal separation between church and state. But those who supported the state of Missouri in its decision to ban funding for the church agreed with the conservative Christian activists on one thing, at least — the case has the potential to affect much more than playgrounds.

“This would be a groundbreaking decision” if the Supreme Court sided with Trinity Lutheran, said the Rev. Barry Lynn, executive director of Americans United for Separation of Church and State.

Lynn, a minister in the United Church of Christ, attended the argument Wednesday, and dismissed as hyperbole ideas such as fire departments not putting out flames at churches. “Fiction, we heard a lot of. Speculation, we heard a lot of,” he said as he left the court.

The fact of the matter, he said, is that the state would be improperly supporting a specific religion if it paid for Trinity Lutheran’s playground. “Obviously this is a promotion of religion,” he said, since the church could use the playground to attract parents to worship there.

“This preschool with its playground attached is an essential part of the ministry of this church,” he said.

Religious groups stand on both sides. The Baptist Joint Committee for Religious Liberty filed an amicus brief in the case arguing that keeping government strictly separate from religious institutions is the best thing for religion.

“Religion has a special place in our constitutional tradition, a place that is protected by separating the institutions of religion and government. The U.S. Supreme Court has never upheld direct government grants to churches, much less required a state to provide such funding,” Holly Hollman, the Baptist group’s general counsel, said to reporters after listening to the arguments in the court. “This case is about whether the state has to pay for the property improvements of a church, despite nearly 200 years of precedent and many practical considerations that argue otherwise.”

Spectators waiting in line to enter the Supreme Court seemed unsure what all the talk about playground safety was about. “I don’t think I can join that group, considering my kid fell out of the monkey bars and broke her arm,” one tourist said.

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