This isn't a thing that I feel there's a uniform one size fits all answer. It's more situational.
For example, I don't care that Heimdall in Thor was black. I didn't really care about the source material, so maybe that's why. But I didn't care that a character had a relatively minor change.
However, I do find it very strange that Katara and Sokka were white in The Last Airbender. What makes it more odd is that the villains were all Indian. It seems like a classic case of White Washing. Especially since Sokka and Katara were fairly dark skinned while the Fire Nation were themselves effectively white. It's very perplexing to see.
Do I get angry at these sorts of things? No, but in the later case, it is a very strange scenario. If the entire thing is changed, like taking a Japanese movie and setting it in Montana, then the changes make sense. Or if finding a suitable actor that fits the race of the character (or if you find someone of a different race who is a perfect fit), that's fine. But changing the character's race just because you can, is where I start questioning the intent.
For example, I don't care that Heimdall in Thor was black. I didn't really care about the source material, so maybe that's why. But I didn't care that a character had a relatively minor change.
However, I do find it very strange that Katara and Sokka were white in The Last Airbender. What makes it more odd is that the villains were all Indian. It seems like a classic case of White Washing. Especially since Sokka and Katara were fairly dark skinned while the Fire Nation were themselves effectively white. It's very perplexing to see.
Do I get angry at these sorts of things? No, but in the later case, it is a very strange scenario. If the entire thing is changed, like taking a Japanese movie and setting it in Montana, then the changes make sense. Or if finding a suitable actor that fits the race of the character (or if you find someone of a different race who is a perfect fit), that's fine. But changing the character's race just because you can, is where I start questioning the intent.