A forum has heard opposing views on the issue
Atheist Ireland say current school admission policies based on religion here are a breach of human rights.
There are renewed calls to ensure children have equal access to schools, as a forum on the role of religion in primary school admissions got underway in Dublin.
It has been organised by the Department of Education and Skills as part of a broader consultation process.
Advocacy group Equate has asked Education Minister Richard Bruton to fulfill his commitment that all children have equal access to and feel safe, protected and supported in our schools.
Equate director, Michael Barron, said: "Debate and consultation is certainly an important part of any change in our education system - yet after a decade of missed opportunities on the issue of religious discrimination in school admissions, we once again stress the need for any outcome to this Forum to be equality and children's rights based.
"Equate believes that the law which allows a child's religion or belief to be used to exclude them from a State-funded school must be amended.
"It is the fairest and best solution to this issue and research has shown the vast majority of parents would like to see this happen."
The Church of Ireland's General Synod Board of Education said it was "grateful for the opportunity to participate".
"Having heard the range of views expressed by all those who participated, the board hopes that the Minister will now fill the information gaps identified by the forum.
"The board also hopes that the minister will bring forward a set of proposals to assuage the concerns held by minority faiths involved in the provision of education on the effects new measures may have on their faith communities", it added.
Two of the people represented at the forum - Michael Nugent of Atheist Ireland and Seamus Mulconry of the Catholic Primary School Management Association - spoke to Newstalk Breakfast earlier.
Mr Nugent claimed Mr Bruton was "fine tuning" discrimination.
"The minister is essentially taking the smallest part of the religious discrimination and privilege in schools - which is in access - and he's just fine tuning that discrimination.
"He's ignoring the vast majority of discrimination and privilege, which is by integrating religion throughout the entire curriculum once you get into schools, and that the Catholic schools are opposed in principle to teaching religion in a pluralistic way.
"He's saying that it's because he wants to protect minority schools - but all he's doing in practice is giving Church of Ireland schools the opportunity to discriminate against Evangelicals, giving Sunni Islamic schools the opportunity to discriminate against Ahmadi Muslims, and essentially giving some of the larger minorities a slice of the discriminating pie."
However Mr Mulconry said it is not about religion, but resources.
"Last year in the 384 Catholic primary schools, there were 7,750 unsuccessful admissions. And of those 97 had to do with the lack of a baptismal cert - so in point of fact this is a problem, not about religion, but about resources.
"There are at least 17 schools in the city that are over-subscribed, and legislation won't solve that problem - we need more school places.
"I have never come across a case of any child being denied access to a Catholic school solely on the basis on the lack of a baptismal cert.
"Where we have space we will take everybody, and we would like more space to be able to take more people".
Mr Mulconry added: "Parents are making more applications than there are schools - they're applying to two or three different schools, and that's one of the key problems.
"We don't know the full level of demand for schools in the greater Dublin area".
But Mr Nugent saifd the issue is about human rights: "We're having a debate with 10 different United Nations and Council of Europe human rights bodies telling Ireland that the way that we run our schools - both in terms of access and in terms of failing to give an objective, critical and pluralistic education that isn't involving religious indoctrination is a breach of human rights.
"One of the most fundamental human rights is the right to freedom of religion, conscience and belief".