No, I do understand what you're saying. I don't think it's wrongheaded, but I think there are more nuances to the comparison.
I'm comparing it to Classical Marxism and internationalism, which as far as I'm aware has always been opposed to rigid social-sectarianism which seems to be the dominant mentality now. By free movement I don't mean the actual EU policy itself but rather the spirit behind such a notion, that people shouldn't be trapped in their culture nor rejected from another's.
I think the more foundational idea of the "spirit," as you call it, is that people can practice their own culture anywhere they choose without being persecuted--not that people outside certain cultural practices can choose on a whim to move within them, somehow. Cultures aren't fixed in the same way that national borders are. When an American visits Australia, they're subject to abide by Australian law, but not to participate in Australian culture.
I think that over time people can change their culture. If a white person marries an Asian person and they move to Asia, maybe over time the white person adopts certain customs and practices. I'm not sure I'm comfortable with a white person just acting Asian temporarily, or some such. That seems less respectful to me and more like entertainment, if not mockery.
I know that some might say that imitation is a form of flattery, but there's a difference between cultural appreciation and cultural amusement. More often than not, dressing up in Halloween costumes is a form of amusement that people by defend by calling it appreciation. To be crude, I think that's bullshit. In many cases, costumes are extremely stereotypical images of particular cultures that don't reflect widespread behavior or common practice. In other cases still, costumes may reflect what said cultures view as specialized practices that most members of that culture wouldn't--or couldn't--perform, much less someone dressing up for Halloween. It may even be the case that someone wearing a costume might intend it respectfully; but in that case, maybe the wearer should take the time to actually back up their "respect" with some research and realize that the costume itself is offensive and/or reductive in specific ways.
Finally, and from a more theoretical angle, while we see white people in America dressing up in various Latino or Asian costumes, we don't see Latinos or black people dressing up in "white American" costumes. It's the case that certain cultural images have been commodified, and commoditification can be read to reflect a cultural hierarchy whereby certain cultures only appear through various festivities, holidays, or costumes. I see this less as respect than as mere toleration, if not amusement.
I do see how criticizing cultural appropriation can be seen as nationalistic, and that might be a contradiction some leftists don't realize. I happen to think cultural appropriation should be criticized, just as I think that national borders are ultimately a necessary aspect of modern global development (fwiw, I wasn't trying to argue against borders in that last big showdown; I was just pointing out what I saw as a contradiction between nationalism and free market ideology).
More egregious forms of what you and others call cultural appropriation (black, red, yellow and brown face for example) are not things I would defend even if I don't agree that those are examples of the concept but rather just low-brow forms of racist entertainment, but a white woman at a prom wearing a culturally Asian prom dress should be an utterly uncontroversial act and an attempt to put a stop to such a practice is IMO a fundamentally nationalistic act.
I agree that this is a more questionable example, especially given that the wearer seemed to have more knowledge/respect for the culture. It wasn't a cheap Halloween costume, it was an expensive dress. And, if I recall, people in China actually weren't upset.
