While I personally have decided to not dabble with words I dont understand and dont identify with, does your statement also mean that Western adaptations of ethnic customs should not be called their original name?
For example, should "yoga" still be called "yoga" if it is practiced by white people in the West?
Well, the statement of mine that you quoted is a statement about exactly what it says it's about; it doesn't 'mean' anything about anything else - the only part of it that's broadly extendable is, 'If the ways aren't old, don't call them "the old ways".'
But 'yoga' is an interesting and illustrative example of the complexities of cultural appropriation, so....
The word 'yoga', as it's used in Western cultures, refers to
Hatha yoga, or, most often, to its asanas (postures) used purely as physical exercise. Since the physical techniques of Hatha yoga are just one aspect of the interlinked set of spiritual, mental, and physical practices that is what 'yoga' refers to in India, it's just plain
inaccurate to refer to the Western practice simply as 'yoga'. The Western practice is not merely an 'adaptation' of the yoga of India, it's a different thing - the yoga of India is not an exercise program.
While people in the Western world will, obviously, continue to use 'yoga' colloquially for the physical exercise, I think it's both less misleading/confusing and more respectful to the source to be clear whenever possible that we mean 'Western Hatha yoga'.
There are other aspects to the matter. On one hand, yoga, and particularly Hatha yoga, was introduced to the West by Indian yogis, so it's not an identical situation to cases in which Westerners have simply grabbed a practice without any training in that practice at all. On the other hand, it's still a situation fraught with the complexities of colonialism and imperialism.
Cultural appropriation is seldom as simple as (as the title of that other thread puts it, though darned if I'll quote the misspelling) 'Yea or Nay'. Things are not just either 'fine' or 'bad' - and there's no authoritative body to rule on it, so 'allowed' and 'not allowed' are meaningless.
This also brings up the issue of non-Norse descendants practicing Asatru, when Asatru is SPECIFICALLY ancestral worship.
As well as what Darkhawk said, I'll note that while ancestor veneration is indeed a core aspect of Asatru, the ancestors one venerates are one's own ancestors, whoever they might be.
To me, it's the same concept as this Totem issue, but no one seems to bring that up here nearly as much Native American appropriation. However, during my years dabbling in Asatru, most people I spoke to said Asatru is open to everyone, regardless of heritage. So where is the line?
As I indicated above, there is no simple, clear line. But in this particular instance, you're comparing the customs of living, but endangered, cultures, with those of a culture that hasn't existed (in the form in which it's being reconstructed) for centuries.
So it's only the same concept if you're assuming that genetics are the key factor - but they're not. The key factor is
culture, and about having the kind of exposure to a culture that allows one to perceive it, and function within it, as a cohesive whole - if one isn't born and raised in it, that takes a lot of learning.
To give an illustration, I am one-quarter Icelandic. My grandmother, who died a few years before I was born, was herself born here, though both her parents came from Iceland as adults; just about the only bit of Icelandic culture that was passed down to me was, we sometimes say, 'Go the notes of the rote' (a secondhandedly phonetic rendition of 'góða nótt Sofðu rótt', which I had to use Google Translate to get the spelling of, that means 'good night, sleep well').
And even if far more of the culture had come down to me, it would be the Icelandic culture of the ~1870s, as filtered through three generations of diaspora. I am not culturally Icelandic, nor would I become so just by reading about modern Iceland and adopting the trappings of Icelandic life; I would need to talk to Icelanders (a lot!), visit Iceland (repeatedly, and for long stretches!) and probably move there permanently, learn to speak and read Icelandic... and no matter how long I spent on it, I would never be as culturally Icelandic as someone born and raised there.
If, on the other hand, I were to listen to Björk constantly, and claimed that doing so meant I completely understood Icelandic culture (which sounds ridiculous when I put it that way - but all too often, the claims of cultural appropriators are just about as substantial as that), I would not be an Icelander, I would be an asshole, and my genetic heritage has nothing to do with it either way.
Modern Icelanders are authorities on modern Icelandic culture, in a way that a non-Icelander (however much Icelandic ancestry they have) can never be. Likewise, the actual members of any living culture are authorities on their culture in a way that non-members can never be. If a culture is no longer a living culture, and thus has no native authorities, the situation is somewhat different (though it's still not necessarily a matter of 'up for grabs by whoever wants to loot the ruins'; if it was a living culture until recently, and your culture was the one that overwhelmed it, 'looting' is exactly the word for it).
That's just a very few thoughts about a very complex topic - and that's why you can't take a single sentence I (or anyone else, for that matter) has said on the subject and try to divine an entire system of intercultural ethics from it.
Sunflower