Yes.
I'm going to start by saying that I'm white. Completely white, though I have Jewish cousins. Brown hair, brown-eyed, fair skinned.
But I believe that I can write a black character. An Asian character. A Native American character. Why? Because it is my license as a writer to be able to do so, so long as my intentions are to portray them as a person, not an exotic or racist caricature of what that race or nationality is. Will I ever know what it's like to be a black person, really and truly? Probably not, because I can't reverse-Michael Jackson and suddenly become a black person and I'm not the type to interrogate someone about their life as a member of a particular race. I'll admit that I've never held a conversation with an Asian person, but I know what the stereotypes are. I can ignore them and actually create a character.
Now, there are obvious differences between white and black people, but those lines are swiftly becoming blurred. People marry whom they want. Black, white, Asian, indigenous, gay, straight, bi, or pan, we can marry anyone we choose. If I decide to make a biracial character who is Lebanese and Eskimo, that's my right. I can make a character look like what I want, make them be who I want.
But there are limits. You can't make them a blatant stereotype. You can't write a story with black kids that only like rap and are in gangs along with white people who are rednecks and have shotguns in the back of their truck. That's not a person. It's a stereotype.
Nearly everyone falls into a stereotype in some way. But if the stereotype doesn't define the character, then it's alright.
That's just my opinion.