I care abt racial depiction - it's too easy to perpetuate racist stereotypes, so we have think thoroughly about how we're presenting race in our stories. We also have the ability - especially with a lack of publisher pressure - to be very diverse, and tell stories that rarely get to be heard, and that's important. Just look at the effect of things like Ms Marvel and Cleverman.
Keeping things vague is okay, and sometimes useful and effective, but I personally don't like it. Often, a 'racially neutral' character is assumed white, or written as white - it's extremely difficult to pull off, especially in a realistic setting, because of how culture, ethnicity, and racism affect a character. It's also not always effective representation for these reasons - it's leaving the work to the readers. You might as well just have white characters that aren't explicitly stated to be white - Harry Potter and Hermione Granger were white, originally, but fandom made them poc. (this is mainly referring to race neutrality that doesnt depict skintone, like homestuck or in a book, not a character who is clearly dark-skinned but with an unspecified ethnicity)
I don't know how much it's about diversity per se. It's more about realism; in reality, the world's not all white (and there certainly weren't white people in ancient Egypt, for example). Focusing on diversity can get confusing too, as it places a story with mainly a white cast, but also a black character and an asian character, for example, above a story with an entirely black cast - technically, the former is more diverse, but that doesn't make it any better representation or more progressive than a story focusing on black narratives. For me, it's more about telling stories that don't get listened to, and creating a character for someone to connect with and relate to that rarely gets that representation.
I don't know what you mean by 'are you okay with whatever the author wants to do?' I mean, in the end, it's their story, they can do what they want. If an author's being racist, I'm not okay with that, and I'd complain. And if their story is unrealistically white, I disapprove, but usually avoid - they're just being predictable and uncreative, and the best I can do is vote with my views. I rarely bother reading stories these days that are unrealistically white, or unfairly prioritise white narratives, because that's how I am and what I'm interested in, and want to support.
Although, when it comes to my own comic, race gets confusing and vague. Obviously, it's a social construct, invented long after the time of my comic (roughly 400BC) - and then, half my characters aren't even human. This leads to a lot of vagueness wrt race. White skin didn't exist in Europe back then, generally, so none of my main characters are white, but they're still ethnically Irish - because of trying to at least vaguely depict an ancient society, representation doesn't really come into it.
That being said, because of the storyline and myths I'm working with there's race parallels. They're not really intentional; I don't want to write a race metaphor, because I'm not trying to say smth abt race with my comic. I'm worried about people trying to compare the oppressions shown in my comic with real life issues, because they're very different. But this means I'm concerned about the messages I'm giving off - if my fictional situation will teach a negative message about real life situations that are similar.
As you can see, I overthink things. This included.
also, wrt your query abt anime's depiction of Japanese people vs Western depictions - western/American cartoons have largely been made by white people, with their depictions of east/s. east asian characters being stereotyped - this coming from out and out racism, and from their default style being the depiction of a white person, so they need to change it to depict an e/se asian person to make it clear. (for example, in daria the eyes are typically lines with dots in them, no whites, which is often how e/se asian eyes are drawn in cartoons of the time - so they have to slant the eyes of e/se asian characters in a way that is stereotypical and exaggerated)
whereas anime is made entirely by East Asian people, primarily Japanese people - so they don't have racist stereotypes about what e asian people look like, and in anime - being japanese - that's the default ethnicity. So they don't default to exaggerated or stereotypical features. (and then, to differentiate, their american characters are hilariously stereotyped and i love it)
also, anime is largely for kids, so the characters have different colours of hair and eyes - not just brown and black - to differentiate, and because pink hair is fun, lets face it.