I am not sure whether ownership is the right way to frame this question. It seems that it might be more perspicuous to think of the question in terms, perhaps, of duties we owe to one another, in terms of respect for other cultures (and others' cultures), or of virtue considerations such as being respectful of others. From these points of view, I think answers are easier to reach: It certainly seems like a kind of violation of a duty to respect others (for example, as an application of one of the ways Kant formulates what he calls the categorical imperative, which mandates treating others as ends only, and never as means), and also seems like the vice of disrespect for others to violate rituals in this way.

Of course, it might also be more complicated, depending upon what motives apply to the apropriation (commencial? for the purposes of ridicule? out of a sense of shared reverence?).