Why do people assume that characters are white? Of course, we first have the problems with racist canons, colonialism, and other claptrap. But then we have the fact that so many stories are set in places where a majority of the people are white. Because white people average more money and education than everyone else, more writers are white. White writers tend to write white characters, or at least, characters easily mistaken for white if not explicitly named otherwise.
Ways to fix this:
* Set stories in places where most or all the people are some other color than white. If a story is set in Africa or China, would you assume all the characters are white? Probably not. It's a very different experience to be black in Africa than in America, to be Chinese in Japan than in China, to be Mexican in Los Angeles than in Idaho Falls.
* Whenever you set a story in a specific city, check its demographics. Compare Los Angeles to Chicago to Montpelier. Each city has its own unique demographic profile. Use this to sort your characters. If there's no reason for them to deviate from the local norm, 10 characters from Los Angeles should be roughly 5 Hispanic, 3 White, 1 Asian, and 1 Black. Plus if you look up countries of origin, you see very different detailing within those broad categories. I have Omaha characters in Nebraska and Miwok in California for a reason. If we make a habit of doing this, people will quit assuming all characters are white unless flagged differently.
* Describe features from the full range of humanity. Skin goes from alabaster through tan and honey tints to terra cotta to brown and black. Hair can be straight, wavy, curly, or nappy. Eyes, noses, and mouths come in many shapes. A character with coily black hair and naturally tan skin probably will not be read as white even if you don't specify African-American or Hispanic or Sicilian. A person with fair skin, curly blonde hair, blue eyes, and a broad nose may well be a "blackfella in a whitefella body."
* Throw in other markers besides appearance. Humans encode culture into basically everything we do -- makeup, clothes, jewelry, music, religion, dialect, etc. A Muslim is probably not white. But a Muslim who listens to hip-hop is probably black while one who listens to beledi is probably Middle Eastern, even if you don't spell it out.
* This also works with every other demographic. Humans are roughly 49% male and 51% female, or slightly less if if you count the 1% or so of trans and intersex people as a separate category. Your stories should show the same mix unless there is a reason not to (e.g. you are writing about a baby shower with all women). About 20% of people have a disability, so unless you have a reason to change that (e.g. you are writing about Gallaudet University), roughly 1 out of 5 characters should have a disability. Demographics are powerful; use them. You cannot fairly be accused of discrimination if you are mapping your representation to the setting.
* With that in hand, consider randomizing elements of character development. I literally diced up most of the major traits for the Blueshift Troupers, and some for Schrodinger's Heroes. It's a fantastic method for ensemble shows when you're starting for scratch. If you're worldbuilding, it works there too.
* Alternatively you can grid characters instead. Frex, make one for each of the 9 intelligences. You can see where I've gone down lists of common causes for chronic pain or types of neurovariance. There are no humans in A Conflagration of Dragons and the races have features (coloration, wings, horns, etc.) based on elemental correspondences.
* Show as much diversity as you can fit into your writing. This will teach your fans not to make assumptions about unspecified character traits. Look at my writing -- if I haven't spelled it out, in most cases it could be anything. Not white. Not straight. Not human. You get the idea. People are complicated, I have to pick and choose what will fit in any given story based on what's relevant to that story. For series where I make character notes, however, there's often a lot more detail (coloration, sex/gender, orientation, etc.) in the character sheet than the story itself. If it's mentioned in the sheet but not the story, that's background parity. Just making sure the story is congruent with the character sheet creates a space for those other traits to exist.
This is one of the few problems that is absolutely, totally fixable. All it takes is people writing more diverse characters -- or prompting them or buying them, if you don't write yourself. If you don't like discrimination in literature, you can definitely stab it to death with pencils.