The Ulster Unionist Party wants to end the teacher exemption of employment law in Northern Ireland.
Currently a Catholic school can discriminate on the grounds of religion when it is taking on new teaching staff.
The UUP says this is "illogical" and has tabled an amendment to a bill currently progressing through Stormont.
If it is accepted the exemption would be removed at it would be much easier for non-Catholics to get jobs in RC schools.
UUP MLA Sandra Overend said: "The Ulster Unionist Party enthusiastically supports the idea that children from all community backgrounds should increasingly be educated in the same classrooms as a matter of course.
"However we would argue that it is illogical to break down barriers between pupils without simultaneously breaking down the barriers between the various school types in terms of teacher appointments.
"A useful first step would be to remove the teaching exemption from Fair Employment regulations.
"Many people will find it amazing that in 2016, it is still perfectly legal to recruit teachers on the basis of their religion."