Historical fiction is a genre near and dear to my heart. As an anthropologist and history buff, I have always had a sweet spot for stories set in the past. The most successful historical fiction writers know they have to make unique considerations for non-white characters.
Your characters do not live in a vacuum. Their settings will be influenced by major current events that happen in their world. Your characters should at the least know about them and at most have a direct involvement in them. If you write a story set in the 1930s United States and you mention The Great Depression, you should consider that The Great Depression affected white and non-white Americans in different ways. The story would be inauthentic for your non-white character if you don't acknowledge that in your story.
When you're doing research about a period and setting consider what your character of color's life would be like. How is it different than your white character and how would it be the same? Do you remember Calpurnia in To Kill A Mockingbird? She was "part of the family" but was kept at a distance. She lived outside of white Maycomb, away from the Finch family, but was a member of the black community.
Here are some tips for creating authenticity when writing historical fiction:
Hire a sensitivity reader. A sensitivity reader will be able to consider how honest your character's experience is in her/his setting.
Consider how your non-white and white characters would interact with one another and why. For example: In 2017 two characters of different races conversing in a doctor's office waiting room but that wouldn't be plausible in 1917 America (even outside of the south).
Major current events will affect your characters differently based on that character's race. Think about the attack on Pearl Harbor. Imagine how a European-American character and a Japanese -American character would handle the aftermath of that event. These are distinct experiences to the same event.
Research what non-white characters were called in the time your story is set in. Unlike whites federal and cultural terms for non-whites has changed over the years.