My take is:
If a character needs to be a specific race to make sense, then they should be that race. You can't tell a story about asian people by having them all be white people. You can't tell a story about black people in America, if there are no black people.
Sequels or prequels should retain the race of the person.
If we're talking about a remake or a new adaptation, then it doesn't matter. The Little Mermaid has no obligation to be white. They're a fictional mermaid, and it makes no sense to apply cultural requirements to something that doesn't exist. There are plenty of stories where they are covering the same kind of material with creative liberties. The Lion King was heavily inspired by Hamlet. No one has issues that a very similar story was told by lions, instead of medieval Europeans. On that note, plenty of Shakespeare's work has been adapted for other countries, other time periods and other races, etc. Yet strangely no one seems to care about those kinds of adaptations even if those changes potentially break the narrative.
Rings of Power, I know that middle earth is intended to be Europe, but black people canonically do exist in that space. There are people (Haradrim) who are supposed to be brown skinned who are present in the Lord of the Rings books. This is also a world where there is magic and shapeshifters, so I feel like it's doubly silly to hold up that standard.
At the end of the day though, I would say the primary issue with "white washing" isn't that a character is played by someone of the "wrong race". It's the fact that there frequently weren't many non-white actors in the first place. Like plenty of Indians looked up to Apu to some extent, because at the time there were so few Indian characters in media; and yet he was played by a white guy.
If we lived in a society where it was pretty normal for Indian, black, white characters to all play each other and any talented black or asian or white actor got the best roles, I think there would be substantially less issue. But we don't.
