I don't support YPG/PKK, but that kind of salute actually originates from ancient Rome, and practiced way before Nazis took over Germany, it's only after WW2 that it was associated with National Socialism.
Let's not call everyone we don't like "Nazis" shall we?
Diplomacy backed by strength works indeed. But if this strength turns into unjustified violence, this leads to horrific situations like World Wars. And this world cannot bear another global conflict as weapons that are capable of destroying entire cities in one volley are around.
Well... we sort of become the successor of the Eastern Roman Empire as a political entity after 1453 but this has nothing to do with being muslim or not.
"Byzantine" is not an ethnicity. It's an Empire which was named after the old name of Constantinople, Byzantion. While the ruling class of the Empire spoke Latin until 7th century, during the reign of Heraclius it hellenized.
What you're doing here is an anachronism.
In anyway, this is war and we should be ready to face its consequences. As long as we are in this conflict we will suffer casulities. This is unavoidable.
Byzantine Empire was much more than just Orthodoxy and its Caesaropapism. What makes the Roman Empire is not its religion, but its governing institutions. laws and bareucracy, which was evlolved during the reforms of Justinian and died out with Latin sack of Constantinople in 1204.