The Catholic education sector will be damaged if academic selection remains, according to some primary school principals.
Catholic bishops have called for politicians to agree on a better system of transfer to post-primary schools.
In a Catholic Principals Association survey, 63% of those who responded agreed failure to end selection would have adverse consequences.
Of the 400 principals written to, 112, or 28%, responded.
Seventy-six per cent of those who responded agreed too much deference was shown to grammar schools.
The survey suggests many principals feel pressurised into using unregulated academic tests even though they feel it undermines church teaching.
While the Catholic bishops want academic selection to be phased out, only one Catholic grammar school has done this, and the Catholic Principals Association (CPA) has become impatient with the slow pace of change.
It said the survey results would make uncomfortable reading for supporters of academic selection.
Most of those who responded to the survey said they felt pressurised to participate in the unregulated transfer tests, in case they lose pupils or staff.
Most believed it was not possible to get good results without coaching pupils, which they felt had a detrimental effect on the curriculum.
CPA chair Michele Corkey said the current system of "perceived losers and winners" was "corrosive of a child's dignity and worth".
She said the survey's findings emphasised that the Catholic system's "ethos, spirit and infrastructure must be founded on specific moral and educational imperatives".
"It is time for all Catholic principals and all church leaders to be more proactive in implementing successive statements by the northern Catholic bishops," she said.