In all honesty it did start with the best of intentions, mostly concerning native american indians (and yes they do like the term indian to be used). It's mostly about not picking up things with rather important religious contexts simply because you think they're cool.
Native american headdress and religious symbols are the first that spring to mind. Also the tribal tattoo fad was extremely difficult for some pacific cultures as tattoos with deeply religious symbols and signs of adulthood were suddenly on the sleeve of every drunken jock or chav.
In this context the nazi's using the swastika is cultural appropriation, which caused obvious issues. Another example would be how religious Hijabs spread outside of the arabian peninsula, first to other areas populated by arabs, but then also non arab islamic countries like egypt, libya, turkey, syria and iran (the burqa however is pre-islamic) in the last 60 years or so, whereas previously in non rural area's of those countries it was often seen as a sign of fundamentalism, barbarism and bad education. Such examples have shown to be very oppressive and offensive with wide spreading consequences.
Then you have where SJW's have gone too far regarding some other things like dreadlocks, pseudo-religious tattoos, clothing, music, speech mannerisms etc. In these cases no-one cares and if someone complains they're a jackass sjw.