It's meaningless when everything we already have is the result of cultural appropriation. This goes for minorities as well, so it's not even a white thing.

Plus if people mix (muh diversity is our strength), culture, food, music, etc. will mix as well and you do not have to explain yourself to anyone.
I used to date a Chilean dude. I was at his place and his mother made us food. Was I supposed to ignore the meal she made to eat toast instead because I'm white? Hell, I helped her cook sometimes. Was I supposed to tell her to fuck off because I'm white? They made me feel welcome and it was a very good experience, it felt like home. (The guy's stepdad is also white, he is this blond Swedish dude lol.)
Lets say we stayed together with the guy and had kids. Are they supposed to eat my white food or his Chilean food? Half and half? Would I have to leave my own kitchen when he cooked? Would I have to tell my own kids I refuse to make the food grandma made because I have no right?

People are complicated and everything you can imagine happens. This includes people with 4 grandparents who are all from different cultures. People in interracial relationships or even people adopted/raised in different cultures. When those mixings happen you get people who look different from what you would expect.

This is the same as with the whole "own voice" trend in writing, when you are only allowed to write people like yourself (race, culture, religion, sexuality, gender, mental health state, etc.). It's retarded and evil to demand people to tell you about their private life so you decide if they are allowed to do something or not. It's private, it's their business.