Falkirk Council's move comes after rising population rates left denominational schools oversubscribed, meaning pupils who are not Catholic will have to use placing requests to get into the schools, even if they live in the catchment area.
Although such schools were originally designed to serve Catholic communities they have a diverse population which includes pupils of other faiths as well as those of no religious background. However, councils still have a legal duty to offer denominational education to Catholic families.
A Falkirk council report on the issue says nearly 40 pupils were refused enrolment to Catholic schools last year, resulting in a growing waiting list for places.
It stated: "It was not possible to reserve any places for pupils likely to move into the area because the demand came from pupils that live in the catchment areas of these schools.
"As a consequence, there are no places available in primary one at several denominational primary schools for Catholic pupils that move into the area, and this has resulted in a growing waiting list for places."
The council said considerable investment had been made in the school estate in recent years to increase capacity, but demand for places had continued to grow to a level that could no longer be met.
It concluded: "We are proposing that the schools admissions policy is changed so that Roman Catholic-baptised pupils will still be entitled to enrol at their catchment denominational school, but all other pupils would have to submit a placing request. This would mean spaces could be reserved for Catholic pupils where necessary."
The Scottish Secular Society has now written to the council urging them not to "discriminate" against children wanting to attend Catholic schools from other faiths or no faith.
A spokesman said: "The council is planning to introduce a discriminatory schools admission policy to ensure children who are baptised into the Catholic Church are given priority over other children getting into these schools.
"Catholic children will need to show a baptismal certificate to prove they are Catholic and any unfilled places will go to children of parents of other religions and none."
Michael McGrath, director of the Scottish Catholic Education Service, said: "There is no national policy on the issue, but councils have put similar strategies in place to ensure Catholic pupils priority get first right of access in rare cases where popular schools are oversubscribed."
If the proposal is backed by councillors following the consultation, the policy will be introduced in December.