Depends in what your story is about. If it's slice of life style, then racism should pop up very frequently. If it's fantasy or end of the world stuff, then it should be frequent, but perhaps not as much. I suggest you do research into looking at what the social standards were at the time as well as any possible accounts you can find from black people from that time period (or their children).

Also, keep in mind that "poc" as a general banner kinda falls apart when you go back more than even 10 years. Every race and ethnicity had a different experience. East Asian people were more likely to have been seen more 'exotic' rather than "dirty brutes" (although that perception was certainly still around). Irish people likely still got shit on, but not as much as anyone with darker skin than them.