On first guess, I would say that we live in a cultural export society. Our goal is to export our culture. How can you appropriate someone's culture while they're busy selling it to you? Not only do we export our culture, we're constantly making more of it by ditching what came before creating something new. It's never the same twice, so you have to buy more of our culture just to keep up.
Now, looking at cultural appropriation in that context, you can see why our culture is very culture blind to the idea of cultural appropriation. To even understand the idea, we have to step outside of our own culture, which is hard. Not only do we need to step, but we need to succeed in our appreciation of their culture.
There's a second problem with cultural appropriation in our cultural context. THEY might be exporting their culture, too. Can you really call it cultural appropriation if you can go to an ethnic store and buy something off the shelf? There's no culture police checking your ID. You can have a genuine, made over there, cultural object to show or wear and they don't care.
Cultural appropriation itself isn't an absolute, but a relative, and that relative increases the difficulty in identifying cultural appropriation. We need to understand the circumstances to understand appropriation, and as you know, ignorance is rampant in our society, with nobody (even us smart ones) knowing everything, leaving us with the guaranteed probability that culture will get appropriated no matter how good our intentions.
A third issue is the rules cultural appropriation itself. Without rules for cultural borrowing or cultural integration, without good guidelines for doing it well, we'll be left doing it badly, and that sends us into cultural appropriation land. It's this lack of a what TO do and this preponderance of what NOT to do that leaves people all frustrated, and once frustrated, good luck getting them to cooperate.
A fourth issue that I see is that cultural appropriation is our culture. That may seem unfair, but that's the truth. People choose these bad cultural stereotypes because that's our culture. We simplify unfairly. Go to a costume store and see what costumes exist for the 60's, 70's, and 80's. That's our own culture that's been mangled and simplified into an insulting but sellable form. We don't just use our cultural appropriation tools against others, we use it against ourselves. How's that for a kicker?
So rather than explain how to avoid cultural appropriation in stories, I'd like to kick about a few touchstones on how to use cultural integration well. (Note that there are always exceptions and reasons to do otherwise. For example, the purposefully offensive comedy is its own art form.)
Note that no rule can create immunity from accusations of cultural appropriation. This is always subjective goal.
Note that many of the guidelines below result in better characters and better books.
Other cultures are cool and fun and interesting and frustrating and stupid. Use them. Enjoy them. Show the fun. Avoid flatting them. When you only show one aspect of a culture, you're dipping into cultural appropriation territory. You've reduced the culture to a monofilm. The more nuanced the culture, the less appropriated the culture becomes. Likewise, when you over-elevate a culture, you also risk cultural appropriation.
Are you stereotyping? Don't. That produces shallow characters who make your writing job harder. Defining a character by nationality, religion, or other organization/subgroup is a sure highway to stereotyping. You are usually be better off defining a character by their name. By avoiding stereotypes, you avoid cultural appropriation. In cultural appropriation, stereotypes simplify characters to a group or gender identity.
A character's competence/quality should not be connected to their culture (or religion, or gender, or anything). Any person may or may not be a good tracker or even a good person simply because he (or she) is a Cherokee. Likewise, a character's competence should not be limited by culture/quality. That Cherokee might have done a stint in the Army as a cook or a sniper, or both.) With cultural appropriation, the character stands for the entire culture. Essentially, the culture is the character.
Character depth should be similar across all peered characters. If all your characters are shallow, then having a shallow character who happens to be a nationality is fair. With cultural appropriation, you have a character with too much or too little depth compared to their peers. Too little and you get stereotyping, and too much and you get cultural wanking.
If you like an element of a culture and you want to use it, then use it. Because you like it, you'll be able to explain it and put it into context. Share you enjoyment with your readers. If you can't explain it to your readers, then learn enough to explain it. With cultural appropriation, elements of culture exist without context, defined entirely by their seemingness.
Groups are not monolithic. Be specific where you can. When you say THEM, you are selecting a large set of people with diverse language and cultures and geographic locations. Those details work to your advantage, so use them. With cultural appropriation, groups and lumped together and simplified.
At the end of your work, the reader should have learned something of the other cultures, traditions, histories, and such. The reader is richer for it. With cultural appropriation, the reader is left no richer. We see the external bits of culture without any of the context. You learn the cook without the rule.
Does that help? Does that make sense? Is any of it even right? Go talk among yourselves.