If your game depicts a real-world culture that is not your own, hire a consultant to make sure you’re respectful and get the details right. It would be best if you also playtested with people from backgrounds related to your theme.
1. Don’t exclude historical facts
World War I and World War II themes have been used many times in board games and war games. But despite this fact, minorities who also participated in these conflicts are rarely depicted. Seeing an entire group of people being removed from history is quite common.
When your game is placed in a historical context or shows historical characters, it is important to document yourself thoroughly. Check your assumptions about what types of people were in different historical settings. There were Black cowboys and Mexican cowboys in the Old West, for example. There were Black people in Medieval Europe.
Also, when characters are inspired by real-life or other fictional characters from other sources, make sure not to replace a character from a minority with a character from the majority. Doing this strips the opportunity for a social group already under-represented to be represented.
2. Sensitive topics
On the other hand, if the historical theme presents a group of individuals from an angle that today could harm its reputation, then ask yourself: does the portrayal of these individuals add value to the mechanics of the game? If your game has an educational purpose, then yes, historical accuracy is essential. Otherwise, be careful not to prejudice these individuals and do not glorify wrongdoings.