In the United States, blackface was used as part of
Minstrel Shows, which is basically a comedy show where the only joke was basically "Wow, black people sure are stupid!" As you can imagine,
incredibly fecking offensive. Blackface was also used on stage or screen so that a show could have black characters, without having to actually, you know, hire black people. The white actors would then usually play up negative black stereotypes in the process.
So there is a lot of history of blackface being used as a method of mocking black people. But, hey, that's just history. Why would it be offensive today?
Your point that you wouldn't be offended by a black person in "whiteface", or that it is the same as wearing a red wig, is what we might call 'false equivalency'; within a larger cultural context, it isn't the same thing. There are several reasons for this.
The first and most straightforward is that the mentality of the ministrel show hasn't disappeared. A lot of people who wear blackface in their costumes for Halloween or whatever use it as an excuse to make fun of black people, so people are wary of it. But that doesn't make in
intrinsicallyracist, right?
Well, no, nothing is "intrinsically" anything when talking about race, because race isn't skin deep. You appear to believe in a sort of colourblind mentality towards race, in that it doesn't matter at all what race you are. Well, race is kind of an absurd concept (see below the break) because humans pretty much just made it up, but humans also just sort of made up things like governments, laws and economies, which are also important and "real" things. So let's talk about race. Really talk about it.
To many people, especially people of colour, race matters. It can matter in a lot of negative ways, manifesting in poor treatment, harassment, or simply the circumstances into which they were born, statistically. It can also matter in many positive or affirmative ways; concepts like "Black culture" or "Black pride" exist as a counterpoint, a way for Black people to take pride in themselves and their experiences, and to explore concepts that dominate culture, white culture, doesn't have experience with that many Black people do. Serious stuff, like mistreatment by the police and justice system, or basic stuff, like hair. Hair! Bet that's something you've never thought about at length (lol) but
it's a pretty important issue for Black folks in America.
To white folks like us, this often doesn't make a lot of sense; we were taught as kids that race doesn't matter. But it's very easy to say that something that rarely seems to affect us doesn't matter; our race as white people is seen by society as default, our experiences as normal. Our stories get to be the ones that get retold and remembered, and we retell and remember them quite frequently. It's like saying it doesn't matter who wins or loses, after collecting the trophy and the prize money.
So something like whiteface doesn't affect us; it's just skin tone, after all. It's also why, as Americans who are very disconnected, often by generations, from our European ancestors, we often don't give a **** about those stereotypes either. I don't give a **** when people make Scottish jokes, and I wouldn't give a **** if people made Czech jokes, if those were jokes people over here made. It's not all that important to me.
If you are a person of colour in America, it is impossible not to notice race. Even if you've never been subject to malicious racism, you know that you are perceived as an outsider to the dominant culture. Even if you didn't want to care about race, race has been made important for you, personally. You've experienced a lot of **** you know is basically invisible to white people because of "just" your skin tone.
So when some white guy rolls along in blackface, or using black slang or trying to use the n-word positively or neutrally, it rings hollow. It's a mockery, somebody who thinks that all you need to emulate this giant, deeply personal and nuanced concept of Blackness is some shoe polish.
That's what's offensive.