I liken deriding cultural appropriation to the concept of racial purity and the creation of a Folkish state free of the cultural corruption of the money-hungry Jew...
In that its an idea that should not be cast aside lightly, but thrown with great force.
Enough historical context makes so much of today terrifying.
As far as I'm aware, though, people deriding cultural appropriation usually mean disrespectful copies of significant works and traditions. Unless they're misguided zealots, of course, which is probably mostly the case anyway.
Wikipedia says that "cultural appropriation" is understood as a situation where a minority group has its cultural values used in a colonial fashion by a dominant group. It's a terribly named term, because any reasonable person would immediately assume from the name that it just means cultural elements crossing over from one culture to the next, or traditions being adopted from different cultures.
The problem as far as I can tell isn't that elements cross over - instead it's that significant things to a culture (a Native American war bonnet in most examples) are copied superficially and without respect to their original cultural/spiritual meaning. It usually requires these things to have a particular cultural or spiritual meaning in the first place, of course, which is why I think making or eating food originally from a culture not quite your own isn't cultural appropriation at all. Making Siddhartha Gautama into a mascot for your car dealership or hawking fake Aborigine ritual objects might be, because quite a few people take those things pretty seriously. Blackface shows are also cultural appropriation because they superficially imitate a minority culture while disrespecting that very minority. You could, for instance, serve bacon dim sum at your restaurant, and that's not cultural appropriation until you start calling it funny names like "ching chong bacon" or something of that nature. And the Color Run isn't disrespectful to Indian culture because it doesn't pretend to be particularly related to Holi or an accurate representation of Indian tradition, just a different use of a similar process. Not so sure about weeaboos, though. I guess the stereotypical weeaboo does base their behavior on often insulting Japanese stereotypes, so maybe?
Point is, the objectionable part of cultural appropriation comes in when you use a position of power to mock something important, and cheapen the original in the process. Of course, there's a different standard of "important" for every person, so if you happen to identify with Chinese-style dumplings strongly enough to feel that any non-Chinese variant of them cheapens your culture (or worse, assume that every Chinese person ought to identify with Chinese-style dumplings strongly enough to feel this way, and then feel insulted on their behalf), well.