An Austrian cardinal is promoting interreligious dialogue, while Turkey is using a historic Christian cathedral as an Islamic house of worship.
A Turkish court recently ruled Hagia Sophia must be reclassified as a mosque.
Many Christians are expressing outrage.
Patriarch Bartholomew of Constantinople: "The conversion of Hagia Sophia into a mosque will disappoint millions of Christians around the world."
Pope Francis says he's saddened by the decision.
Cardinal Christoph Schönborn of Vienna is echoing the pope's concern. But the cardinal wants the former cathedral to be a hotspot for ecumenism, remarking, "It would be a dream if Hagia Sophia became a center for the encounter of religions. It would be a victory and a blessing for everyone."
Hagia Sophia (Greek for "holy wisdom") is a Byzantine cathedral built in the sixth century in Constantinople (modern-day Istanbul), and turned into a mosque in 1453 after the city fell to the Ottoman Empire.
Nearly 500 years later, it became a museum in 1934.
Schönborn has come under scrutiny for hosting pro-LGBT events at St. Stephen's Cathedral in Vienna.
The cardinal turned 75 — bishops' mandatory retirement age — earlier this year, and says the search for his successor is well underway.