Cultural appropriation is a broad enough term to functionally be meaningless, but I've found it helpful to think through 4 distinct interests at play, that I think are legitimate:
Proper attribution/credit. We don't like plagiarism or unattributed copying in most art. Remixes, homages, reinterpretations, and even satire/parody are acceptable but we expect proper treatment of the original author and the original work. Some accusations of cultural appropriation take on this flavor, where there's a perceived unfairness in how the originator of an idea is ignored and some copier is given credit. For a real world example of this, think of the times the fans of a particular musical artist get annoyed when a cover of one of that artist's song becomes bigger than the original.
Proper labeling/consumer disclosure/trademark. Some people don't like taking an established name and applying it outside of that original context. European nations can be pretty aggressive at preserving the names of certain wines (champagne versus sparkling wine) or cheeses (parmigiano reggiano versus parmesan) or other products. American producers are less aggressive about those types of geographic protected labels but have a much more aggressive system of trademarks generally: Coca Cola, Nike, Starbucks. In a sense, there's literal ownership of a name and the owner should be entitled to decide what does or doesn't get the label.
Cheapening of something special or disrespect for something sacred. For certain types of ceremonial clothing, wearing that clothing outside of the context of that ceremony seems disrespectful. Military types sometimes get offended by stolen valor when people wear ranks/ribbons/uniforms they haven't personally earned, and want to gatekeep who gets to wear those things. In Wedding Crashers there's a scene where Will Ferrell puts on a fake purple heart to try to get laid, and it's widely understood by the audience to be a scummy move. Or, one could imagine the backlash if someone were to host some kind of drinking contest styled after some Christian communion rituals, complete with a host wearing stuff that looks like clergy attire.
Mockery of a group. Blackface, fake accents, and things of that nature are often in bad taste when used to mock people. It's hard to pull this off without a lot of people catching strays, so it's best to just avoid these practices. With costumes in general, there are things to look out for, especially if you're going out and getting smashed.
