Blackface isn't always about caricature, we see this most frequently in Hollywood, but it wouldn't be the first time I've seen a white person wearing dreadlocks or even a traditional Nigerian outfit.

That's just a person who likes Nigerian culture, it's not someone claiming that they are Nigerian.

Blackface itself is a little rarer, but being tanned to look like someone from the Mediterranean is still very popular

That's just adjusting your skin tone for fashion. If i asked someone getting a tan what they were doing they wouldn't say "I'm becoming Greek".

likewise White-face is an entire make-up industry with various skin lightening products. It's okay to want to make yourself look white but woe betide anyone wants to actually look black, nope, must be a caricature.

Because the cultures whom do that aren't mimicing a different ethnicity, but attempting to lighten their skin because in their own culture light skin typically meant you didn't labour outside.

What do you do if a white kid wants to be a dark elf at a party? Same goes for cosplayers.

Yes, culture identity is the same as playing a fictional game?...

The point Rowling was making, well okay, if it's not acceptable under any circumstances to attempt to change your race, even if you 'feel' like that race, then why is it acceptable to change the gender.

Because the systemic nature of sexism and racism are completely different. You cannot change your "race" because that particular social construct involves actual shared lived experiences particular to each society. Part of belonging to that particular culture is that shared experience. There is no common shared experience that includes every woman in every society. Women of different societies have vastly different shared life experiences depending on their individual cultures.

good faith matters and blackface isn't always caricature

Blackface is definitionally always a caricature....

"Blackface is the practice of non-black performers using burnt cork or theatrical makeup to portray a caricature of black people on stage or in entertainment"

Engaging in black America's culture, or enjoying African culture is not blackface. The fact that you are conflating the two is either very ignorant, or intentionally racist.