Not for a long long time, and it was never exclusively true. Although I will give you that there was racism back in the day, but that really changed more than 60 years ago, and has improved ever since.
Sure, they can be played by any character. It's not been about whether a mermaid could be played by a black character. It's whether there is a double standard, and that if there was a story featuring a black character, would there by bitching about it from the Left if a production changed it to white. I think we all know there would be.
That you don't know, because (a) it's not known if there really was a Jesus in real life - there is zero proof, and (b) even if there was one, if we're basing it on the available genetic possibilities at the time, he could very well have been more Greek,Macedonian, Philistine, or other local ethnicity than "hook nosed Jew" as you suggest. We don't really know where his family came from, and there was plenty of mixing.
Sure, but Ariel is the subject of an old fairy tale, and in the actual tale she is definitely described as white with long straight hair, sufficient to actually clothe her. So, as a piece of Scandinavian culture, it is what the Left would - in the reverse situation - call "cultural appropriation." Again, it's really the double standard people are identifying here.
John Leguizamo should play whatever part he and those producing a movie think he should play, and if they want to create a unique production where John Leguizamo portrays Adolph Hitler or Czar Ivan the Terrible, go for it. But the reverse should also be true, and it doesn't have to be a hispanic actor playing Fidel Castro. Fidel was white hispanic. And a lot of people could play him and still be true to skin tone, but even if a black or Irish ginger actor were to play him in a different production it should be fine.
The trouble is all the bitching about this issue and the focusing on it being one-sided - in other words, when the Left applies its "progressive stack" mentality to the issue, it then becomes a grievance list of who gets to complain - and of course - white men don't get to complain - well the straight ones, anyway - but everyone else does. We need to jettison that bullshit.