Ann Willey, who has been at the cathedral for nine years, is leaving after a departmental review at the Minster which has been operating at a deficit for the past three years.
The chancellor of the Minster, the Rev Canon Professor Edward Norman, wants a "change in emphasis" in the service provided by the centre for school visits.
Peter Lyddon, chapter clerk, said: "We have to make sure that we are not bashful in putting out the Christian message. There's a danger of treating the cathedral as a heritage centre."
The centre for school visits has tried to introduce the cathedral to children as a place of worship and also use it to reflect aspects o the curriculum.
Mrs Willey said: "For many children this is their first experience of a Christian place of worship. You don't go in heavy-handed, indoctrinating and trying to convert them.
"We have built up credibility with teachers that while reflecting the Minster as a Christian place of worship that is not what we are doing to their children."
Her redundancy is said by both sides to be amicable but schools voiced fears about the future of the organised tour and support provided by the centre.
The Minster, however, says organised school visits are safe. Teachers will now be sought to act as volunteers for the guided tours and to work in the centre.
"The service will be just as good if not better," said Peter Lyddon.