It's pretty easy to fall into a black and white, "clash of civilizations" mindset- but the idea that Muslims and Christians will always clash while helping their coreligionists is a falsity currently and historically.

Especially in zones of contact between the two religions, such as the Balkans and the Eastern Mediterranean over the last 1,500 years or so, we see people are just as likely to put personal gain or even cross-religion family ties over ideas of religious brotherhood.

Just for a few examples: The original tribal confederacy that created the Ottoman state was made up of several Greek Orthodox family groups alongside Turkish Muslims ones. After the House of Osman became dominant, the Christian families were slowly phased out of leadership roles. Later, the Ottomans were brought into Europe by the Byzantines as a support against Christian Slavs who were then besieging the Christian Byzantines. The Byzantines would even marry their princesses to the Muslim Ottomans to shore up the alliance.

Much later, it was not uncommon for Ottoman statesmen who had been born Christian and levied as Janissaries to keep in contact with family members who had stayed Christian. There are examples of Grand Viziers who stayed in regular contact with Christian family members in Serbia or Venice. The Ottomans were in heavy contact with neighboring Christian states. They were allied with the French for hundreds of years against the Habsburgs. In response the Habsburgs tried to put together an alliance with the Persians. Sultans would take taxes in Parmesan Cheese because they liked it so much. Traders, military men, architects, etc would regularly go back and forth between the Ottomans and their Christian neighbors.

This doesn't even mention the close proximity that Muslims and Christians lived in throughout the Balkans and Anatolia. They got along pretty well until the age of nationalism started breaking it apart. I don't want to paint too rosy a picture, but our current preoccupation with assuming Muslims and Christians are opposites that have never had much contact and always put religious brotherhood ahead of personal reasons or pragmatism is objectively not true, especially when we consider how much interaction has gone on historically.

Check out "The Nature of the Early Ottoman State" by Heath Lowry for the early Ottoman period and "Contested Conversions to Islam: Narratives of Religious Change in the Early Modern Ottoman Empire" by Tijana Krstic.