Delegates at the primary teacher union's annual congress in Derry have mandated the INTO to seek that the requirement for the so-called religious certificate be done away with.
They have also instructed their union to survey members on whether they believe Catholic faith formation should take place in schools and whether primary schools should have secular or religious patrons.
Around 93% of primary schools in Ireland are Catholic and the requirement that teachers have this certificate and qualification is seen as a barrier to employment for teachers who are not Catholic.
In a heavily supported motion, delegates also instructed the union to form a task force to look at the future of primary school patronage and to examine the results of the survey.
Speakers told the congress that Irish society has changed and that schools must too.
Teacher Jason Kenny said that schools needed to suit all children but that currently children are being obliged to suit their school instead.
Teacher Peter Melrose told the congress of an interview he did earlier this year for a job at a Catholic school.
"When I went to the interview the very first question I was asked was about religious instruction", he said.
"I was made to feel uncomfortable for several minutes and eventually I just gave up and gave an answer that represented myself truthfully and authentically. I was unsuccessful in my interview," he added.
Referencing the current teacher shortage, he said he saw that post readvertised and a couple of weeks ago he saw that that post was still unfilled.
"There were questions about religion [asked of me] that I felt deeply uncomfortable within 2024.
"People who feel like me have very little choice when it comes to where to teach," he said.
Teacher Anna Hurley spoke about how she was no longer a practicing Catholic and how both of her children who attend a Catholic school have "opted out" of religious instruction.
"Discrimination is the daily reality for thousands of teachers and children in classrooms throughout the country", she said, referring to the fact that children who are not Catholic and do not want to participate in Catholic religious instruction are given no alternative programme to follow during that time.
"When I ask other parents who are non-practising why they have not opted out their children they tell me 'I don’t want them to be the odd one out’," she said.
Fionnuala O’Regan told delegates that "for a truly diverse workforce, we need to find flexibility around the requirement for a religious certificate".
One speaker said he hoped the fact that he was speaking in favour of this motion would not "tell against him" with his employers.
After the debate, Anna Hurley told RTÉ News there were many teachers who would have liked to have spoken but who had not out of fear of repercussions for their jobs or careers.
Teachers are legally obliged to uphold the religious ethos of their school.
Just four teachers spoke against the motion.
One of those speakers said she wanted "to remind [all delegates] of your obligations to your patron body".
Siobhán Lynsky said that over a career of 33 years she had been asked at every job interview she ever did "will you uphold the Catholic faith".
Ms Lynsky spoke against only one section of the motion which set a timeframe for completion of the survey that she felt was too narrow.
"Support the motion yes," she said, "but please give people time to complete the survey".
Teacher Annemarie Collins, who is a Traveller, also spoke against the motion.
"I am for it, but I am also against it," she said, as she outlined how it was not religion that was stopping Travellers from becoming teachers but the narrow academic requirements laid down by the Teaching Council.
"I think the religious certificate should be gotten rid of," she said, "but I know so many Travellers and they are getting money from their parishes [to help them become teachers]."
"I would not be a teacher only for the fact that the Christian Brothers funded me," she said.
Teacher Tomás O’Reilly from Roscommon, who proposed the motion, said all teachers were asking for was a voice.
He pointed out that parents were being surveyed on the issues of the religious patronage of their schools and said teachers views should be canvassed too.
"Personally I am a Catholic but I would prefer if the schools were secular. That is my personal opinion but honestly what I would really like is that people would have a choice. Parents would have a choice and teachers would have a choice," he said.
While one section of the motion which stipulated that the survey should be completed by next month fell, the rest of the resolution was overwhelmingly carried.
After the debate teacher Tara O’Callaghan told RTÉ News that she had felt emotional during the debate such are her feelings on the issue.
"I am a practicing Catholic who has been to Medjugorje several times and I feel the job of faith formation is too important to be given to schools and taken away from parents," she said.
Strongly criticising a system that "others" some children in the classroom because they are not Catholic and are not therefore involved in preparing for sacraments such as Communion, she said: "I taught in second class and I know how much time sacramental preparation takes."
Another teacher, who also described herself as a committed Catholic said her own child, who is being raised as an atheist was being "othered" in his classroom.
She said this was not his teacher’s fault but the fault of the system.
A striking feature of the discussion has been the number of teachers who say they are Catholic but do not support the current system.
The motion is a significant one for the INTO. It gives the union a clear mandate to pursue an issue that teachers to date have been relatively silent on.
The INTO has been instructed by its members to now directly engage with the Catholic church to seek an end to the requirement that all teachers in their schools are qualified to instruct children in the Catholic faith.
The union leadership will now have to come up with a strategy to reflect the motion but the issue has been clearly placed on their agenda by members.