In many rural areas, the answer is simply that the only option is a Catholic school. Furthermore, the enrolment policies of these schools discriminate on the basis of religion, and give priority to Catholics and allow a place to non-Catholics only if the school is not oversubscribed.
The most recent Organisation for Economic Co-operation and Development (OECD) Education at a Glance report found that Irish primary schools teach two-and-a-half hours of religious education a week compared to just one hour of science.
In fact, Irish primary schools devote 10pc of teaching time to religion. This is second only to Israel and is more than double the OECD average of 4pc.
Mum Dorothy Kelly didn't want her son Oscar (4) to go to a religious school. She describes herself as having no religion and feels that it is disingenuous of people who don't participate in Catholicism to baptise their children, and that it is also disrespectful to the Church.
She decided to send Oscar to the Montessori Education Centre in Dublin city centre. It is a multi-denominational school. Dorothy says: "It follows the Montessori method and religion just doesn't really feature in that."
Mum Carla Bannon prefers to be called humanist to atheist. She says: "I find the explanations that lie in science and rationale to be far more satisfactory than those put forward by any religion. From a morality point of view, I believe we are all wholly responsible for our own actions, without any reference to the supernatural."
Carla knew before her first child, Siun (4), was born that she would not baptise her but, with the nearest multi-denominational school 15km away, that she would probably have to send her to one of the local Catholic schools.
"I didn't, however, realise how actively they espoused the religion and how much it permeated the day-to-day workings of the school and how difficult it was to avoid," Carla says.
"I'm unhappy with her learning Catholic doctrine when her father and I have so many issues with it, both in terms of a belief system and the Catholic Church's views on so many issues which are at polar opposites to ours," she says.
While Carla is happy with the school in general, she feels that the lack of choice afforded secular families is unacceptable.
"Children are being indoctrinated against their parents' wishes and parents are having to accept this in order not to undermine their children's place in the school community and it's not right. Faith formation should be left to families and churches."
Jane Donnelly, of Atheist Ireland (www.atheist.ie), explains that Catholic schools' admissions policies breach the human rights of secular families.
"Under human rights law, it is forbidden to discriminate against secular parents and children on the grounds of religion in the education system. The Irish State is obliged to ensure that all children have access, without discrimination, to a local school as education is a human right," she says.
Donnelly says that the primary school curriculum also breaches human rights as it speaks of the role of religious education in enabling children to come to a knowledge of God.
For those who have no option but to send their children to a Catholic school, Donnelly argues that the State has a constitutional obligation to allow children to opt out of religious education and a responsibility under the European Convention to ensure that children are supervised during this time.
However, she says that this rarely happens. "The right to opt out of religion in Irish schools is a theoretical illusion and not operable in practice.
"Consequently, secular parents cannot ensure that the teaching of their children is in conformity with their convictions and are denied their basic human rights."
Last year, the Minister for Education, Ruairi Quinn, established the Forum on Patronage and Pluralism in the Primary Sector with a view to transferring up to half of the country's Catholic primary schools to other patrons.
In the Irish school system, a patron is the legal entity that establishes a school and has ultimate legal responsibility for it. As a result of the forum, parents of school-age children in 44 areas around Ireland are soon to be surveyed on their preferences for primary school patronage.
Educate Together (www.educatetogether.ie) is the patron body of 65 multi-denominational primary schools in Ireland. CEO Paul Rowe says that in Educate Together schools "children are equally respected irrespective of their social, cultural or religious background".
Rowe says that the upcoming surveys should encourage a wider discussion on this issue than ever before.
"If successful, this survey approach should lead to a balancing of the choices available to parents in the selected areas so that the needs of all families are met.
"This should lead to a better balanced and more vibrant education system."
Educate Together will open its first second-level schools next year.
Parents interested in sending their child to an Educate Together school can visit the website to see if there is an existing school or a start-up group in their area.