Getting It Right
(I assume by the question that you are white. Forgive me if that's inaccurate. Whether you are or not the opinions in this piece apply.)
I think a better way to phrase the question might be, "Should white writers write characters from other races/nationalities?"
I say this because here in America "other races/nationalities" are completely inundated with images, depictions, writing, and even interactions with the majority race. We see you day in and day out. We work with you, we live around you, we cannot simply choose to not engage with the America’s hegemonic culture, which, at least for the moment, is still white culture.
So, we can write about you without missing a beat for example Grey's Anatomy. The show was on for years before we were all surprised to find it was created and written by Shonda Rhimes, a black woman. It was and is one of the best shows on ABC. So, clearly we can write about you. Because we know you. Whether we've wanted to or not there is no way we can avoid that education. But you can. You can intentionally wrap yourself up in a soft, white blanket and sleep deeply in a world where black and brown hues don't exist.
So, here is my point. If you want to write about characters from other cultures make sure, damn sure that you have, like all writers should, done your research. That includes reading the writing of, talking to members of, actually learning the history and background of, and immersing yourself into the culture you intend to write about. Don't do them, yourself, or your work the disservice of getting it wrong or worse yet offending people because you haven't taken the time to respect the people you're writing about. That would be the mistake of an amateur, right?
Be intentional about getting it right.
BTW, one show that got it so very right with African American characters is This is Us. I was so shocked and pleased with how right they got it so I looked up their writers. Two of the four are African American.