It depends on your metaphysical presumption about what constitutes theft. That is some people say will say yes, and others will say no. A wise person recognizes there is no way to determine which is right or wrong without making a value decision.
Let's start with the definition of appropriate. From Google:
take (something) for one's own use, typically without the owner's permission:
So, the question you ask is really does one group of people have the right to behave in a way another group of people behaves without their permission.
I would suggest that in a free and democratic society, the answer is broadly no, unless a specific harm can be demonstrated. In the US, for instance, rights are enumerated in a Bill of Rights adjacent to the US Constitution that guarantee people free speech. That's not unqualified, but that means if one group begins to talk one way, the second group has a right to mimic their speech regardless how the first group feels about it. If their speech is symbolic, then the second group's actions are also protected. If the first group wants to assemble, the second group can also assemble. If the first group publishes ideas, the second group can publish the same ideas, albeit in a different way. If the first group forms a religion, the second group has a right to use the ideas and form a similar religion. What's the common currency? Maximizing freedoms without harming.
That brings us to the question of whether or not one group can consider their uncomfortable feelings harm. According to the article, harm consists of:
pain, death, disability, mortality, loss of ability or freedom, and loss of pleasure.
For the most part, mimicking others causes little way in harm, though certain exceptions might decided.
- You cannot ape someone in a way consist with assault and battery.
- You cannot mimick someone if it violates their copyright or harms their protected status.
- You cannot literally impersonate them and steal their identity.
These, exceptions, are difficult to show as harmful at the cultural level. The best examples of these damages might be money to be made from speech or behavior at the expense of others. Many famous bluesmen who were black and second-class citizens in the US before the Civil Rights Era, for instance, made little money, though the art form of blues and eventually rock, made many white men wealthy.
But what harm is had by dressing like another culture? Speaking like another culture? Organizing like another culture? Should a poor country who begins to use cell phones be considered appropriating the culture of a rich country because the rich country invented the phones? Should a colony be forced not to speak English as a second language because they are attempting to improve their relationship with their colonizer, England?
Thus the whole notion of cultural appropriation is hard to define, and often is contingent upon one groups "feelings" and "emotions", which is notoriously non-objective. In this way, it becomes easy for a small minority of people to impose a tyranny on others by simply labeling anything they perceive as imitation and don't like cultural appropriation. From the article:
John McWhorter, a professor at Columbia University, criticized the concept in 2014, arguing that cultural borrowing and cross-fertilization is a generally positive thing and is something which is usually done out of admiration, and with no intent to harm the cultures being imitated; he also argued that the specific term "appropriation", which can mean theft, is misleading when applied to something like culture that is not seen by all as a limited resource.
The question, therefore, is is cultural appropriation really a form of theft, or is it merely a regular and positive occurrence of imitation. And this is contingent upon your notions of theft.