I'm noticing a thing. If someone says, "Wow, I like cheese, must be my Italian background," it is cute if you are Italian. One imagines it's tongue in cheek, because we all (one hopes) get that Italians are not genetically required to like cheese, but Italians certainly might have been raised in a food culture that often features cheese. But, if you were for example Chinese and loved cheese, and said, "I must be secretly Italian", it's a little less funny. Now of course, I have swapped out the power dynamics, the Chinese do not have a history of say, showing up in Italy and declaring it theirs, or mining the good stuff and shipping it home as far as I'm aware. (The Chinese are certainly not innocent of colonialism.)
And why so serious, it's only a joke. Except it's not really funny. Because we're reinforcing bad ideas about people only being able to like and appreciate a culture if there are of that culture. This is why you see so many pretendians, folks who have decided outside of any and all genealogical evidence that they are secretly Native American or First Nations, because those ideas speak to them. This is why you get people claiming their are transracial who are not transracial adoptees.
You can like and appreciate things that are not genetically yours. You can like and appreciate things that differ from how you were raised, or who you grew up with. And I get this is like the adult version of if you love cheese so much you should marry it, but you can love cheese and not marry it. I swear!
Where this really becomes problematic, is when people then decide their bone deep affinity for a thing means they get to do things that only folks of that culture should do. You can't use words that are offensive, that have been used to oppress. Your affinity is not an all access VIP pass. You can love it deeply, fully, wholly, and still be respectful. And if you can't, then you didn't really love it. You just loved pretending.