Wouldn't their Islamic army kill them for doing this?
Depends on the year. The only point I see this occurring is in the very early 1300s under Osman. This however would likely just lead to the Ottoman state being a defensive vassal of Byzantium.
Not going to happen. Muslims converting is anathema, and you'd have to have a Christian empire take the territory over, and effectively prevent the killing of converts. Good luck with that.
Moreover, if some other Empire rules the area, and Anatolia slowly converts over several centuries, how is this 'Ottomans' converting.
So. No.
Depends on the year. The only point I see this occurring is in the very early 1300s under Osman. This however would likely just lead to the Ottoman state being a defensive vassal of Byzantium.
In almost any religion it is disliked to convert, like uhh. Having a out of reach Turkmen is not too hard and foreseeable, having anyone convert in a stage of pre eminence is unlikely but in the early periods this was not the case.
What's the latest the Ottomans can convert to Christianity? How would it happen?
The early Turks stay Tengriist longer and later convert to Greek Christianity due to their leaders decisions. They eventually conquer Anatolia and erect a Christian kingdom. Later the Turkish Christian Empire has an emperor , a Caesar- a Sezar (Sezar is Türkisch for Caesar, the Slavs adapted Caesar as tsar)
Ya. But that long predates Osman. So, while that could be a TURKISH Christian state, it's not an OTTOMAN Christian one.
???
Having Ottoman TERRITORY convert (back) is entirely possible, although it would take a while. Having the OTTOMANs themselves convert isn't.
If the ruling family converts, the power structure will depose them. So you have to replace the power structure, and therefore, almost certainly, the family.
Similarly, if a Carolingian, Capetian, Plantagenet, Bourbon, Hapsburg or Hohenzollern converted to Islam, they too would be deposed.
So "Hapsburgs/Carolingians/Capetians/Plantagenets/Hohenzollerns convert to Islam" is trivially more likely than Ottomans converting to Christianity, but astronomically improbably.