Ireland opened its 400th multidenominational primary school in September, a milestone the Department of Education marked with a modest press release and that campaigners marked with a mixture of pride and arithmetic. Four hundred is a lot of schools. It is also 13 percent of the total, in a country where fewer than half of adults under 35 describe themselves as practicing Catholics.

“Twenty years ago there were 30 of these schools, and people said we were a fringe,” said Niamh Brennan, the chief executive of Educate Together, the largest multidenominational patron body. “Now there are 400, and in half the towns in Ireland there is still no choice at all. Both things are true.”

Of Ireland’s roughly 3,100 primary schools, 2,730, or 88 percent, remain under the patronage of the Catholic Church, which appoints their boards, sets their ethos, and until a 2018 law could give priority in admissions to baptized children. The church’s share has declined by only four points in a decade, because almost all of the new multidenominational schools are new buildings in growing suburbs rather than existing schools that changed hands.

The government’s plan to transfer existing Catholic schools to other patrons, announced in 2012 with a target of 400 transfers, has produced 28. The process requires the consent of the local bishop, a survey of parents, and a willing new patron, and in practice stalls on the first. “Bishops are not opposed in principle,” said Aoife Nolan, a principal officer at the department who oversees the program. “They are opposed in every particular case.”

The Rev. Declan Murphy, a spokesman for the Catholic bishops’ education office, disputed that characterization. He said dioceses had offered 110 schools for transfer since 2020 and that in most of them a majority of parents had voted to keep the Catholic patron. “The narrative is that the church is clinging on,” he said. “The reality is that parents in Ballinasloe or Tralee, who could choose otherwise, mostly do not. We serve the families who are there, including the ones who do not come to Mass.”

Ciarán Walsh, 41, a software engineer in Naas, County Kildare, said that was the problem. His daughter attends the local Catholic school because the nearest Educate Together school has a waiting list of 90 names. “She is doing First Communion preparation in class time, and I am not Catholic and neither is her mother,” he said. “The school is kind about it. She can sit at the back. She is 7. She does not want to sit at the back.”

The department has said it will change the transfer process next year to allow a transfer when a majority of parents request it, regardless of the patron’s view. The bishops have said they will oppose the change. Ms. Brennan said she expected the 500th school in about four years. “We will have a cake,” she said. “And then we will go back to Naas.”