They share food, words, customs and attitudes. That's the common heritage.
Joining Ottoman empire is just a non sequitur.
Joining Ottoman empire is just a non sequitur.
Perhaps it's just the language difference. For example, nobody here would say the native americans and non-native americans have the same heritage. We've been living with natives for hundreds of years, but certainly american heritage stems from britain while native american heritage doesn't. You'd be mocked ( a la Elizabeth Warren ) or canceled if you claimed american native heritage when you are not native american.
Seems like a lot of people are upset for no reason. But when politics and identity are involved, that's just what happens.