Immigrants changing things to fit the new culture and environment is absolutely not "cultural appropriation."

Indian food in America tastes different in many cases not because anything has been appropriated but because it's cheaper to get peppers from the Caribbean...and those aren't quite the same as peppers from India. (And then there's the entire vindaloo mess ;)).

Pizza is another classic example. Italian pizza is different from American pizza. And most people in America forget pizza was ever Italian. But American pizza was created by Italians messing with their traditional food. You could argue pizza has been thoroughly appropriated but nobody ever calls it that. Not a terrible idea to remember every now and then where it came from, though ;).

And then there's people changing recipes intentionally to appeal to white customers. It's amazing how different food from the Thai place suddenly tasted after the first time I ordered from the Thai menu...they started giving me the real stuff ;).