Muslims don’t have a history of converting churches or religious buildings of other religions into mosques. The Hagia Sophia seems to be one of the exceptions.
This tradition goes right back to the capture of Jerusalem in 637 AD.
According to later narratives, after the Siege of Jerusalem in 637 by the Rashidun army under the command of Abu Ubaidah ibn al-Jarrah, Patriarch Sophronius refused to surrender except to the Caliph Omar (579-644) himself. Omar travelled to Jerusalem and accepted the surrender. He then visited the Church of the Resurrection (today better known as the Church of the Holy Sepulchre) where Sophronius invited him to pray inside the church, but Omar declined so as not to set a precedent and thereby endanger the church's status as a Christian site. Instead he prayed outside, on the steps east of the church. The first Mosque of Omar was later built at that site, as evidenced by a stone plate with a Kufic inscription found in 1897 in the area of the eastern or outer atrium of the Constantinian (4th-century) Church of the Resurrection, defining this area as a mosque.
Historically, Europeans don’t have the same record of allowing mosques, until the last few decades. Large Christian communities have existed in Muslim countries from the beginning of Islam, like in Egypt, Palestine, Iraq etc. On the other hand, Muslims were usually exterminated in Europe, like in Spain, Russia etc.
Muslims don’t usually accuse Christianity of being at war with Islam. We may criticize US, UK, France etc. but we don’t call them “Christians.”
Having said that, the ongoing Western assault and destruction of Muslim lands is still going on. European Christian civilization (NATO) is at war with the Muslim world. Israel is a Jewish dagger plunged into the body of Islam.
In such circumstances it is unreasonable to expect Muslims to show benevolence and hand back a cathedral. Maybe one day, hope against hope, the Christians will take the Jews back where they came from and there will be peace and brotherhood between Christians and Muslims.
Then I would hope that the people of Turkey will hand back Hagia Sophia to Christians.
