Best practices in portraying racism and its effects in a game

This question and its fantastic answers help answer NPC interactions with PCs. However, the question doesn’t really touch on a world building, immersion level. I don’t anticipate my players playing a race where these kind of interactions will happen to them. Though, NPC to NPC interactions are likely to have racial undertones (or even overtones).

I’m running a steampunk game that is attempting to be accurate to history and the party will be starting out in New Orleans in the 1880s. Some background of the quest involves a feud between two rich families, one white and proud of it, the other black and do their best to help the black community prosper in these post-Civil War times.

How should I best portray racism involving real-life communities as a white individual? How can I portray the effects of racism (e.g. limited education to a lot of black individuals)?

Obviously I can go the full monty and mimic something along the lines of the movie Django Unchained, with its usage of racial epithets and violence, or using the manner of speech along the lines of what Samuel L. Jackson’s character used in public.

However, white people using the n-word is a touchy subject, and it seems like mimicking certain speech patterns stereotypes racial groups, which is also uncool.

The question boils down to: how can I maintain accuracy and immersion involving racism without stepping out of line?

Assume that the group is okay with the portrayal being extreme though are of the opinion that obviously racism is bad. (I actually haven’t brought up the subject or had a session 0 yet. I’ll most likely mention it tomorrow when the group meets for a different game.)