A lot of it has to do with respect - for the song, for the character, and in some cases for yourself. It can depend on the song. In some cases an oppressed group has enough in common with a different oppressed group, so the underlying spirit of the song transfers easily.
There are some songs I would happily sing but there are others, that are specific to a particular struggle, where I would feel that I was being patronising. I am culturally and racially too far removed from being a black South African to feel comfortable singing certain types of first person song. This doesn't mean I didn't fully support their position aginst apartheid.
Only you can make a decision as to where you stand with a specific song.
Quack!
GtD.