I don't see a situation where "blacking up" is right. There isn't a good reason to blackface, yellowface, brownface, or redface. Skin colour isn't a costume, an ethnicity isn't a costume, some cultural, particularly sacred, clothes are not costumes. There are plenty of ways to dress up without those - doing so reduces people to those features, and reduces important qualities (in people and in cultures) to 'a bit of fun' which shouldn't happen.
I find it odd that many people seem more concerned about the discomfort it causes them to be accused of being a racist than the pain of those being oppressed by racism. As if being accused of messing up (and everyone's does sooner or later, particularly in a society built on and continuously benefits from oppression) is somehow worse than the acts of racism/oppression themselves.
The guilt thing is lame. No one is asking white people to feel guilty. No one asks men to feel guilty. No one asks able-bodied people to feel guilty. No one asks cis people to feel guilty. No one asks heterosexual people to feel guilty. And so on. Because feeling guilty doesn't do anything, it does not help.
I do ask people to apologise when they mess up rather than make excuses - we're human in screwed up society, it's gonna happen. Listen, do research from the many free valid sources on the internet from people from these groups who want to educate (those who want to, not everyone does, don't ask random people) as well as many good books and educate yourself (schools don't teach this kind of thing well right now if at all neither does the popular media), educate/speak out/question your own people when they say crap. Use the power position to help those who don't have it and try to minimize the oppression others have to go through, don't add to the weight.
I've smile and nodded through many offensive actions towards me, it comes with the territory of living in this society - I can't win: I go along with it and I'm used as an example of what everyone 'like me' thinks, speak against it and I'm an example of a bad over sensitive one, not the norm. I get no clout unless someone else (white) speaks with me. This happens, today. People are harassed, abused, degraded, and treated as less than, today. The often quoted 'women make X on what a man earn' is only discussing white women, it gets worse beyond that. People are killed for their skin colour and the association with it, today. Speaking about these things as if they are all in the past invalidates and ignores the pain people go through, today, and prevents recognising and fixing the problem tomorrow (can't fix what you can't see).
And because it is of interest, the Depp thing, He said his great grandmother was "Creek or Cherokee or something". It was a vague throwaway comment in an interview, he not a part of either of those nations or is there any evidence of it (he was adopted by one part of the Comanche nation after he got the part but that's highly controversial as held by the NDN media). He could have used his considerable Hollywood clout to get often overlooked Native Americans actors into the part or to actually use actual Comanche attire rather than a white man's inspired painting that's more a caricature than anything connected to a real Indigenous nations; however, after what happened to Marlon Brando I'm not surprised. We've also got Cloud Atlas choosing to spend ridiculous amounts of money to CGI yellowface White faces into Pacific Asian rather than pay Asian actors. Representation is important, it's been shown that people make a lot of assumptions of people from their media representations and people make assumptions about what can be from what they see up there...which is why media has been shown to lower the self esteem of every group but white boys. And people think there isn't a problem today.