Buzzfeed recently published an episode of Hella Opinions and in it, a group of black people said that whites could use it if it meant they could stop being racist and that woke was just for them to use. Honestly, it's just a word and I believe anyone can use it for whatever they wish although it's often used by activists.
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Guys, I can't find a link for it because I'm not sure the episode has aired yet. If you look at buzzfeed main Instagram though, it will be one of the top posts (probs 5 or so down). It is a podcast and the part they posted is only a little snippet of it.