The Education Minister has announced plans which would effectively bar Catholic schools from discriminating against non-Catholic pupils.
Richard Bruton says he wants to ease the religious bar on school admissions, so that it can only be implemented if the school's ethos is at stake.
The plan would see schools from minority faiths allowed to use religion as a selection criteria in certain circumstances, but those from larger faiths forced to ignore the religion of their pupils.
The Department of Education says there are "complex legal and constitutional issues which will have to be worked out" in order to implement the proposals.
According to the department, the goal is to ensure that religion cannot be used as an admissions criteria in the vast majority of Irish schools.
The Catholic Church currently controls around 90% of the country's schools.
Schools run by minority religious groups, meanwhile, account for 6% of Ireland's primary schools, and multi-denominational schools account for less than 4% of schools.
The department notes: "In very rare scenarios where due to unique demographic circumstances (for example among Border communities with majority non-Catholic populations) Catholic schools find their ethos under threat, it is intended that they will be able [...] to continue to use religion as a criterion in admissions, if they are oversubscribed."
The minister says his proposal strikes a middle ground.
He explained: "I believe it is fair.
"It is providing a fair way of providing options for parents of children of no denomination, or indeed of a different one from the local school, to get a reasonable access to the school."
He added that the plan would not impact the rights of other parents "who want to have their children educated in a particular ethos".
"The aim is to meet the wishes of non-denominational parents – who now amount to well over 10% of their cohort – without unfairly impinging on the rights of other children”.
The Educate Together group welcomed today's announcement.
CEO Paul Rowe said in a statement: "Of course every child should be able to attend their local school - but, crucially, their local school should treat all children with equal respect both at the school gates and in the classroom, regardless of religious, social or cultural background.
"It is Educate Together’s position that simply eliminating the exemption used by religious-run schools to discriminate against non-baptised children in their enrolment policies will not resolve the fundamental structural issue in Irish education."
The Church of Ireland's education board said the proposals recognised the "specific concerns raised by minority faiths on the impact of new measures on minority faith schools".
"The Board of Education looks forward to the detail of the proposals and to engaging with the Minister and his officials in relation to the measures and proposed legislative changes," it adds.
Children and family rights organisation EQUATE, meanwhile, said the issue of the baptism barrier should be dealt with in admissions legislation currently before the Oireachtas.
The organisation's director Michael Barron argued: “While we acknowledge this as progress we remain committed to ensuring that a child’s religion or non-religion is never a factor in their acceptance to a publicly funded school.
“Our published constitutional advice demonstrated that there is no constitutional right to unconditional public funding for all denominational schools."