I'm happy for the Germans to mock our tea drinking, monarchy and parliament.
Huh? What?
Oh, sorry, i was distracted by...
my tea.
And our 300 years of tea culture and our
purpose built tea rooms.
Heck, i can even make these and i can do it well. Which makes me roughly the perfect daughter-in-law.
Oh. Wait. I have to get my fedora...
everybody (except oda) said:
You have kinda missed the essential point: The imitation.
This may be tricky and individual cases may be debated at some length, because essentially it's all about the perspective of the appropriator.
If you immitate without proper understanding
and without integrating the thing (whatever) into your own cultural context with the purpose of artificially draping you into your idea of the culture you are borrowing from, that can and often will be a mockery that is at times indeed comparable to blackfacing.
This does not apply to most of the things that have been cited as examples here.
You can eat all the pizza and all the (radically modified) sushi, peking duck (whatever) that you want. And Japanese musicians can wear a coat and tie and perform classical European music on originally European instruments.
They're not white-facing, because, that's the kicker, they're not doing it to be or feel European.
Similarly a zillion blonde Japanese teanagers and Korea-plastic-surgery-#1 are not white-facing either.
That's the point with the belly-dancing.
Western yoga is essentially gymnastics with a funny label. It has changed. And it is virtually completely devoid of rāja yoga. That's fine.
The Western belly dancers however (most of them) are
not integrating the belly dance into their own culture. And they are not persueing a faithful rendition of the custom in its original cultural context.
It's pretty hard to fail at both, to not do either. You kinda have to do it on purpose. And they do. And typically, to fail at both, you have to use the custom to immitate, to fake immerse you into your fantasy of the original culture.
Now that may still be "not ok" but "mostly harmless" in some cases.
But then comes the context of American and British interaction with the middle east...