Catholic and Muslim leaders meet at the Vatican this week, hoping to improve ties. Christians’ right to practise in Muslim countries has been a sore point in relations – illustrated by the case of one particular church.
From the outside, it looks just like any other church.
But St Paul’s church in Tarsus, south-eastern Turkey, is actually a museum controlled by the government.
Christian campaigners want it to be handed over for religious use.
But the Turkish government has told the BBC that is “out of the question”.
The church is so significant because it stands in Tarsus, the birthplace of St Paul. His status as a towering figure in the history of Christianity means the town is a growing centre for Christian pilgrimage.
But at the moment, access to what was once the town’s church is tightly controlled by the Turkish tourism ministry.
Local Catholics living in Tarsus have to travel almost 30km (20 miles) to the next town to worship on Sundays.
Although religious freedom is guaranteed by the Turkish constitution, Catholics point to restrictions on owning property as just one example of the obstacles they face.
Sister Maria, one of the very few Catholics still living in Tarsus, showed me round the inside of the museum.
She told me how she would love it to be returned to its original function as a church, so that local Christians and pilgrims would be able to worship there whenever they wished.
She was keen to point out that she faces no problems from local people in Tarsus: they know she is a Christian nun, and she enjoys good relationships with her Muslim neighbours.
The mayor of Tarsus has worked to raise local awareness of the town’s Christian heritage, and told me he would be happy for worship to happen freely in the church.
But, he said, any decision would have to be made by the Turkish government.
This might just have been a local debate among Turkish Catholics, were it not for the intervention of the Archbishop of Cologne in Germany, Joachim Meisner.
He has raised the stakes in this dispute, by contrasting the freedoms enjoyed by Muslims in his city with the restrictions faced by Catholics in Tarsus.
As it happens, most of the Muslims in Cologne are of Turkish origin, and they are currently planning a large new mosque in the city, replacing the dilapidated premises where they currently worship.
The new mosque’s radical design – by a Christian architect – includes uniquely shaped minarets, and a structure designed to reflect the community’s stated desire to be open and transparent.
That has not prevented substantial opposition from local people, led by the group “Pro-Cologne”, which fears what it calls the eventual “Islamisation” of the city.
It objects to the mosque, saying its construction is a political statement about the growing influence of Islam in Germany.
Church and civic leaders, meanwhile, have been quick to support the mosque, but believe that the freedom of religion that exists in Germany should also be the norm for religious minorities in Islamic countries.
For Turkey, as it eyes membership of the European Union – knowing it would be the first predominantly Muslim country to join – this dispute is an uncomfortable reminder of how its provision for religious minorities differs from that of its Western neighbours.
But for now, the Turkish government is leaving no room for doubt: it will retain control of the church, and continue to operate it as a museum.
It has, however, made one concession in response to Catholic demands: for a limited time, pilgrims visiting the museum can enter free of charge.
It is not what campaigners were hoping for – but they are determined to continue their fight to regain control of a building that means so much to them.